id
string | setting_key
string | difficulty
string | level
int32 | messages
dict | ground_truth
string | dataset
string | omega_split
string |
|---|---|---|---|---|---|---|---|
math_arithmetic_matrix_determinant_level_6_6_300
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6
|
{
"role": [
"user"
],
"content": [
"Determine the value of det(A) where A =\n[[-11, -8, -29, 13, 21, -8, -21, 30, 19, 25],\n [0, 14, 29, -20, 20, -19, 5, 30, 2, -18],\n [0, 0, 8, -24, -26, -24, 4, 25, -15, 25],\n [0, 0, 0, 25, 4, -14, -21, -5, 11, 7],\n [0, 0, 0, 0, 21, 15, 29, -23, 27, -16],\n [0, 0, 0, 0, 0, -9, 26, 0, -18, 17],\n [0, 0, 0, 0, 0, 0, -1, -16, 25, -5],\n [0, 0, 0, 0, 0, 0, 0, 18, -15, 16],\n [0, 0, 0, 0, 0, 0, 0, 0, -14, 1],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 19]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
600
|
math
|
train
|
math_arithmetic_matrix_determinant_level_6_6_301
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6
|
{
"role": [
"user"
],
"content": [
"Determine the value of det(A) where A =\n[[13, 0, -3, -6, -8, 0, 6, 0, -16, 11],\n [0, 10, 9, 10, -10, 8, -11, 23, 6, 6],\n [-3, 9, -14, -18, 6, 8, 12, -6, 13, 24],\n [-6, 10, -18, -22, 16, -20, -5, -23, 5, 23],\n [-8, -10, 6, 16, -10, -6, 10, 12, -12, 16],\n [0, 8, 8, -20, -6, 16, 10, -10, 22, 19],\n [6, -11, 12, -5, 10, 10, 7, 12, 12, -2],\n [0, 23, -6, -23, 12, -10, 12, 10, -2, 2],\n [-16, 6, 13, 5, -12, 22, 12, -2, -29, 24],\n [11, 6, 24, 23, 16, 19, -2, 2, 24, -2]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
197
|
math
|
train
|
math_arithmetic_matrix_determinant_level_6_6_302
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6
|
{
"role": [
"user"
],
"content": [
"Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[14, 20, 22, -5, 8, -14, 2, -20, -11, 6],\n [20, 11, 4, -6, 21, 1, -14, -8, -8, -18],\n [22, 4, 5, -24, -8, 24, -6, 6, 10, 0],\n [-5, -6, -24, 16, 18, -15, 26, -16, -24, 18],\n [8, 21, -8, 18, -7, -22, 0, 0, -1, -12],\n [-14, 1, 24, -15, -22, 26, 2, -26, 3, -5],\n [2, -14, -6, 26, 0, 2, -18, -9, 17, 9],\n [-20, -8, 6, -16, 0, -26, -9, -6, 18, -18],\n [-11, -8, 10, -24, -1, 3, 17, 18, 20, 15],\n [6, -18, 0, 18, -12, -5, 9, -18, 15, -25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
718
|
math
|
train
|
math_arithmetic_matrix_determinant_level_6_6_303
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6
|
{
"role": [
"user"
],
"content": [
"What is the determinant of the matrix:\n[[-6, -6, -28, -27, -29, -23, -1, -18, -28, 20],\n [0, -3, -20, 0, -17, 7, -6, 12, 17, 9],\n [0, 0, -19, -21, -18, 27, -30, -8, 3, 9],\n [0, 0, 0, -11, -13, -9, 9, 11, -1, 16],\n [0, 0, 0, 0, -28, 1, 14, 2, -23, -8],\n [0, 0, 0, 0, 0, -18, 26, 24, -20, 25],\n [0, 0, 0, 0, 0, 0, -20, -14, -26, -1],\n [0, 0, 0, 0, 0, 0, 0, -14, 7, 6],\n [0, 0, 0, 0, 0, 0, 0, 0, -15, -21],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 27]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
800
|
math
|
train
|
math_arithmetic_matrix_determinant_level_6_6_304
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6
|
{
"role": [
"user"
],
"content": [
"Compute |A| for the matrix A =\n[[20, -22, -14, 13, -4, 7, 18, 9, -10, 16],\n [-22, -14, -11, 20, -24, -26, 6, 0, -20, -25],\n [-14, -11, -4, -14, -14, -6, 6, 0, 2, 18],\n [13, 20, -14, 7, -3, 0, 23, 21, 21, 6],\n [-4, -24, -14, -3, 25, 2, 10, 4, -12, -10],\n [7, -26, -6, 0, 2, -27, 14, 2, 12, 10],\n [18, 6, 6, 23, 10, 14, -24, 13, 2, -6],\n [9, 0, 0, 21, 4, 2, 13, 28, -8, 4],\n [-10, -20, 2, 21, -12, 12, 2, -8, -27, 19],\n [16, -25, 18, 6, -10, 10, -6, 4, 19, -26]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
578
|
math
|
train
|
math_arithmetic_matrix_determinant_level_6_6_305
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6
|
{
"role": [
"user"
],
"content": [
"Compute |A| for the matrix A =\n[[20, -3, 26, -17, 6, -29, 3, 30, 29, 2],\n [4, -27, -28, -15, 23, 24, -27, -30, -2, 3],\n [-16, -28, 1, 20, -9, -22, -1, -1, -7, 1],\n [-12, -1, 29, 3, -10, 27, 24, 23, 20, -30],\n [-18, -5, 28, 15, -20, 12, 19, -30, 10, -19],\n [12, 24, 11, -18, 25, 21, 13, 22, 12, 23],\n [-8, 25, -15, 20, -6, 15, -15, 5, -16, 2],\n [3, 27, 23, -26, 22, -13, -8, -1, -10, -19],\n [-30, -20, -25, -13, 23, -7, 26, 17, 20, -1],\n [-10, -17, 6, 26, -29, 3, 9, 12, -30, 10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
934
|
math
|
train
|
math_arithmetic_matrix_determinant_level_6_6_306
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6
|
{
"role": [
"user"
],
"content": [
"What is the determinant of the matrix:\n[[10, 25, -10, 2, 8, 8, 1, 26, -12, -7],\n [0, -25, -10, 16, 22, -27, 27, -19, -16, -3],\n [0, 0, -10, 27, -14, 6, 8, 19, -5, 29],\n [0, 0, 0, 1, 13, -29, 30, 1, 16, -29],\n [0, 0, 0, 0, 12, 0, 15, 17, 19, 24],\n [0, 0, 0, 0, 0, 20, -15, 14, 17, 6],\n [0, 0, 0, 0, 0, 0, -21, 12, 30, 20],\n [0, 0, 0, 0, 0, 0, 0, 29, -23, 4],\n [0, 0, 0, 0, 0, 0, 0, 0, -7, 9],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -27]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0
|
math
|
train
|
math_arithmetic_matrix_determinant_level_6_6_307
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6
|
{
"role": [
"user"
],
"content": [
"Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[21, -9, 4, -15, 4, -18, -21, -28, 9, -14],\n [0, -29, 27, -16, -27, 20, -14, 8, -15, -12],\n [0, 0, -29, -5, 18, -4, 13, -1, 12, 20],\n [0, 0, 0, -24, -20, -30, -23, -17, 11, 7],\n [0, 0, 0, 0, 1, -13, 8, 10, -26, -13],\n [0, 0, 0, 0, 0, 19, -21, -6, -10, 16],\n [0, 0, 0, 0, 0, 0, 3, 15, -27, 4],\n [0, 0, 0, 0, 0, 0, 0, -21, -25, 10],\n [0, 0, 0, 0, 0, 0, 0, 0, -22, -16],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 29]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
296
|
math
|
train
|
math_arithmetic_matrix_determinant_level_6_6_308
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6
|
{
"role": [
"user"
],
"content": [
"What is the determinant of the matrix:\n[[10, -9, 20, 10, 4, 6, -10, 16, 26, 2],\n [-9, 20, 14, -18, -11, 6, 5, 15, -2, -8],\n [20, 14, 19, -1, -10, -15, 8, 12, 1, -16],\n [10, -18, -1, -7, 4, 4, 15, -18, 8, -6],\n [4, -11, -10, 4, -14, -20, 10, 10, -13, -12],\n [6, 6, -15, 4, -20, -4, -12, 0, -1, 0],\n [-10, 5, 8, 15, 10, -12, -13, 0, 4, 0],\n [16, 15, 12, -18, 10, 0, 0, 15, -18, -5],\n [26, -2, 1, 8, -13, -1, 4, -18, -12, -16],\n [2, -8, -16, -6, -12, 0, 0, -5, -16, -26]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
576
|
math
|
train
|
math_arithmetic_matrix_determinant_level_6_6_309
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6
|
{
"role": [
"user"
],
"content": [
"Compute |A| for the matrix A =\n[[12, -4, 5, 23, 5, 25, -20, 8, 25, 2],\n [1, 14, 27, 25, -2, 9, -7, 19, 27, -6],\n [-17, -28, -1, 4, -5, -13, -18, -14, -17, 3],\n [-5, -2, 25, -18, 3, 27, -30, -10, 4, 15],\n [30, 13, 2, -7, -19, -8, 5, 6, 16, -21],\n [-27, 17, -14, 20, -2, 1, -23, -29, 8, 27],\n [-27, 8, 28, 24, 23, 14, 0, 21, 0, -13],\n [30, 19, -27, 11, -29, 17, -11, 20, 5, 15],\n [-30, 11, -20, -15, 20, -1, -30, 10, 11, 12],\n [14, -10, -3, -26, 6, -13, -5, -1, -12, 27]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
436
|
math
|
train
|
math_arithmetic_matrix_determinant_level_6_6_310
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6
|
{
"role": [
"user"
],
"content": [
"Compute |A| for the matrix A =\n[[23, -26, -16, -25, -19, 29, 17, 22, -5, 2],\n [-27, -10, -24, -2, 7, 8, 26, -20, -8, 18],\n [23, -17, -10, 20, -2, 14, -28, 28, -29, -20],\n [-18, 15, -16, 30, 2, 8, -6, 0, 20, 11],\n [-10, 20, 7, 25, 14, -3, -10, -26, -7, -14],\n [23, 26, 29, 19, -17, -1, 6, -12, 28, 9],\n [-16, 5, -2, 18, 30, 29, -5, 16, -14, 15],\n [17, -9, 5, 19, -26, -8, 6, 28, 6, 0],\n [10, -3, 3, 23, -6, 26, -24, -4, 13, 8],\n [-13, 18, -15, -21, -29, 29, 19, -29, 12, -12]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
231
|
math
|
train
|
math_arithmetic_matrix_determinant_level_6_6_311
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6
|
{
"role": [
"user"
],
"content": [
"Compute |A| for the matrix A =\n[[-24, 2, -2, 20, -6, 1, -6, -3, -10, -3],\n [2, 0, -6, -10, -18, -2, 8, 10, 4, 18],\n [-2, -6, 28, -6, -15, 24, 14, -12, -2, -17],\n [20, -10, -6, 16, 16, -4, 5, -2, -6, -3],\n [-6, -18, -15, 16, 27, 20, -1, -25, 12, -10],\n [1, -2, 24, -4, 20, -28, 20, 14, 20, -2],\n [-6, 8, 14, 5, -1, 20, 17, 5, 16, -24],\n [-3, 10, -12, -2, -25, 14, 5, -14, -2, 20],\n [-10, 4, -2, -6, 12, 20, 16, -2, 17, 20],\n [-3, 18, -17, -3, -10, -2, -24, 20, 20, 27]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
137
|
math
|
train
|
math_arithmetic_matrix_determinant_level_6_6_312
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6
|
{
"role": [
"user"
],
"content": [
"Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, -14, 14, -23, 17, 23, 4, -10, 11, -24],\n [0, 4, -10, 2, 28, -7, 19, -19, 13, -10],\n [0, 0, 29, 7, 29, 7, -8, 11, 26, 30],\n [0, 0, 0, -26, 21, -3, -14, -22, 8, -11],\n [0, 0, 0, 0, 11, -3, -21, 25, -18, 12],\n [0, 0, 0, 0, 0, 27, -24, 15, 10, 14],\n [0, 0, 0, 0, 0, 0, -26, -22, 5, -15],\n [0, 0, 0, 0, 0, 0, 0, -5, -28, 11],\n [0, 0, 0, 0, 0, 0, 0, 0, -27, -19],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
400
|
math
|
train
|
math_arithmetic_matrix_determinant_level_6_6_313
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6
|
{
"role": [
"user"
],
"content": [
"Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, -5, 27, 15, 12, 19, 7, -30, -3, 14],\n [-22, 11, 20, -30, 2, -2, 14, -7, -2, -22],\n [9, 24, 30, -16, 1, 22, -10, -14, -13, -22],\n [17, -2, -2, -4, 28, 7, 23, 7, 23, 10],\n [-7, 21, 30, -29, -24, 28, -10, -17, -9, -25],\n [-29, -14, 27, 30, 29, -24, -7, 10, -26, 9],\n [0, -28, 17, 30, -30, -12, -11, 12, -30, 20],\n [-26, 27, -17, -2, -5, -23, 30, -11, 6, -26],\n [4, 24, 16, 5, 2, -13, 16, -19, 20, -11],\n [-28, 17, 3, 0, 19, -25, 6, -4, -6, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
326
|
math
|
train
|
math_arithmetic_matrix_determinant_level_6_6_314
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6
|
{
"role": [
"user"
],
"content": [
"What is the determinant of the matrix:\n[[10, 15, 30, -2, -2, -30, -7, -21, -6, -9],\n [20, -13, -30, -25, 7, 30, 28, 25, -8, 24],\n [-13, 14, 2, 4, 7, -16, -11, 27, 29, 2],\n [-19, -8, -19, -7, -10, 1, -28, -21, -9, -23],\n [-5, 17, -13, 20, 30, -10, 5, -20, -24, 0],\n [-22, 8, -5, -12, 2, -29, 20, 17, 6, 12],\n [24, 23, 30, 24, -6, 14, -17, -19, -6, -21],\n [-18, 24, 5, -14, -17, -3, 28, -13, 13, 14],\n [17, -15, 29, -30, 0, 27, 4, 20, -5, 17],\n [-8, -16, 28, -1, -17, -5, 1, 20, -9, 8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
494
|
math
|
train
|
math_arithmetic_matrix_determinant_level_6_6_315
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6
|
{
"role": [
"user"
],
"content": [
"Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-18, 15, 17, -11, 20, 22, -10, -17, 28, -23],\n [0, -7, -8, 17, 14, 11, -3, -26, 29, 21],\n [0, 0, -21, -8, -22, 11, 29, -14, 6, 14],\n [0, 0, 0, -25, 17, 1, -30, -23, -12, -24],\n [0, 0, 0, 0, -20, 9, -1, -5, -27, -14],\n [0, 0, 0, 0, 0, -23, -5, 21, -21, -27],\n [0, 0, 0, 0, 0, 0, -1, 30, 30, -30],\n [0, 0, 0, 0, 0, 0, 0, 19, 4, 3],\n [0, 0, 0, 0, 0, 0, 0, 0, -11, -5],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0
|
math
|
train
|
math_arithmetic_matrix_determinant_level_6_6_316
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6
|
{
"role": [
"user"
],
"content": [
"Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[23, 5, -27, 11, -25, 9, 25, 6, 21, 17],\n [0, 26, 12, -24, 9, -1, 21, 23, -1, -30],\n [0, 0, 19, -30, -8, -6, 2, -22, 20, -5],\n [0, 0, 0, -8, -5, -25, -1, -20, 3, 21],\n [0, 0, 0, 0, -20, 2, -12, 28, -2, -25],\n [0, 0, 0, 0, 0, 22, 24, -4, -26, -22],\n [0, 0, 0, 0, 0, 0, 18, 15, -19, -25],\n [0, 0, 0, 0, 0, 0, 0, 16, -20, 0],\n [0, 0, 0, 0, 0, 0, 0, 0, 10, -25],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
600
|
math
|
train
|
math_arithmetic_matrix_determinant_level_6_6_317
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6
|
{
"role": [
"user"
],
"content": [
"What is the determinant of the matrix:\n[[-18, 10, 29, -26, -5, -26, -18, -28, -1, -9],\n [0, 12, -23, 4, -16, -4, 18, -14, 21, -17],\n [27, 1, 0, 23, -12, -20, 29, -6, 14, 7],\n [23, 25, 17, -16, 30, 11, 9, -17, 9, -20],\n [-14, -21, 12, -18, 1, -12, -16, -26, -16, -26],\n [-30, -23, 7, 8, 28, 16, -1, 12, -25, -13],\n [-19, -23, -27, 9, 14, -25, 16, -30, 21, 29],\n [-19, -4, -28, 26, 2, -26, -27, 0, 9, 3],\n [15, 5, -24, -28, 27, -12, -6, -8, 19, 30],\n [30, -28, 9, 30, 2, 6, 27, 27, 14, 7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
218
|
math
|
train
|
math_arithmetic_matrix_determinant_level_6_6_318
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6
|
{
"role": [
"user"
],
"content": [
"Compute |A| for the matrix A =\n[[-19, 10, -7, 16, -12, 10, 12, 8, 29, 7],\n [10, 13, 1, -1, 10, -2, 12, 4, -1, -1],\n [-7, 1, 18, -10, 11, -16, -4, -28, -12, -14],\n [16, -1, -10, -12, 6, 14, 16, 1, 8, 0],\n [-12, 10, 11, 6, -15, 1, 4, 10, 3, 16],\n [10, -2, -16, 14, 1, -29, 14, -16, 6, 0],\n [12, 12, -4, 16, 4, 14, 15, -27, -1, 2],\n [8, 4, -28, 1, 10, -16, -27, 18, 22, 7],\n [29, -1, -12, 8, 3, 6, -1, 22, -9, 28],\n [7, -1, -14, 0, 16, 0, 2, 7, 28, -11]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
250
|
math
|
train
|
math_arithmetic_matrix_determinant_level_6_6_319
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6
|
{
"role": [
"user"
],
"content": [
"What is the determinant of the matrix:\n[[-27, 16, -2, -1, 8, 11, -22, 1, -25, 1],\n [0, -15, -8, 6, -10, 22, -27, -4, -27, -9],\n [0, 0, 20, 11, -24, 6, -30, 1, -30, 25],\n [0, 0, 0, -8, -15, -27, -17, 19, -28, 1],\n [0, 0, 0, 0, 2, -16, -2, -16, 30, -27],\n [0, 0, 0, 0, 0, -8, -22, -7, -6, -2],\n [0, 0, 0, 0, 0, 0, 7, -3, 19, 26],\n [0, 0, 0, 0, 0, 0, 0, 11, -5, 12],\n [0, 0, 0, 0, 0, 0, 0, 0, 9, -28],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 28]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
200
|
math
|
train
|
math_arithmetic_matrix_determinant_level_6_6_320
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6
|
{
"role": [
"user"
],
"content": [
"Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-21, 13, 12, -24, -2, -12, 2, 4, 4, 16],\n [13, 30, 18, -12, 19, 6, 12, -22, -29, -13],\n [12, 18, 25, -2, 11, -27, 6, 18, 8, 0],\n [-24, -12, -2, -13, 2, 4, 14, 24, -21, 10],\n [-2, 19, 11, 2, 24, -4, -12, 0, -14, 0],\n [-12, 6, -27, 4, -4, 4, 12, 22, 12, 4],\n [2, 12, 6, 14, -12, 12, -5, 25, -3, -8],\n [4, -22, 18, 24, 0, 22, 25, 21, 3, 18],\n [4, -29, 8, -21, -14, 12, -3, 3, 9, 2],\n [16, -13, 0, 10, 0, 4, -8, 18, 2, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
309
|
math
|
train
|
math_arithmetic_matrix_determinant_level_6_6_321
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6
|
{
"role": [
"user"
],
"content": [
"What is the determinant of the matrix:\n[[17, -21, 0, 22, 1, -8, 19, -21, 24, -30],\n [0, 15, -26, 20, 22, 7, -5, 13, -4, -30],\n [13, 10, 30, 1, -19, -2, -30, -19, -9, -16],\n [22, 29, 8, 26, -10, -28, -11, 22, 19, -3],\n [6, 9, 20, 14, 26, -24, 1, 19, -17, -4],\n [-11, -14, 11, 7, -13, -29, 20, 13, 26, 9],\n [5, -14, 0, 14, 10, 21, 26, 13, -22, 8],\n [19, -25, -19, 19, 28, -5, 20, 18, 17, 25],\n [23, -23, 6, 18, -16, -11, 9, 25, 23, -21],\n [1, 23, 10, -29, -4, 4, -30, 27, 26, -9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
588
|
math
|
train
|
math_arithmetic_matrix_determinant_level_6_6_322
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6
|
{
"role": [
"user"
],
"content": [
"Determine the value of det(A) where A =\n[[12, 19, 4, -4, 1, 7, -2, 12, -4, 24],\n [19, 30, -1, 22, 18, 8, -14, -3, 0, -8],\n [4, -1, -22, -4, 28, 3, -6, -8, -2, -12],\n [-4, 22, -4, -15, 3, 4, 2, -14, 17, -18],\n [1, 18, 28, 3, 10, 4, -27, -23, 12, 16],\n [7, 8, 3, 4, 4, 30, 0, -14, -16, 19],\n [-2, -14, -6, 2, -27, 0, 1, 8, -6, 0],\n [12, -3, -8, -14, -23, -14, 8, -16, -16, 10],\n [-4, 0, -2, 17, 12, -16, -6, -16, -30, -1],\n [24, -8, -12, -18, 16, 19, 0, 10, -1, -12]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
874
|
math
|
train
|
math_arithmetic_matrix_determinant_level_6_6_323
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6
|
{
"role": [
"user"
],
"content": [
"Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-16, 23, 7, -8, -30, -29, -27, -12, 4, 17],\n [0, 19, -14, 22, -8, 8, 6, -18, -17, 27],\n [0, 0, -18, 19, 7, 16, -11, 18, 17, 11],\n [0, 0, 0, 7, 17, -3, -15, 4, -6, 21],\n [0, 0, 0, 0, 7, 27, -17, -8, 14, -13],\n [0, 0, 0, 0, 0, 5, 11, -11, -15, 7],\n [0, 0, 0, 0, 0, 0, -26, -13, -18, -12],\n [0, 0, 0, 0, 0, 0, 0, -8, 5, -5],\n [0, 0, 0, 0, 0, 0, 0, 0, -26, 24],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
760
|
math
|
train
|
math_arithmetic_matrix_determinant_level_6_6_324
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6
|
{
"role": [
"user"
],
"content": [
"What is the determinant of the matrix:\n[[-12, 8, -3, -16, 29, -9, 17, -21, 16, -18],\n [0, 17, -29, -27, 29, 15, 13, -22, 15, -13],\n [0, 0, 6, 2, 21, 18, -6, -8, -27, -25],\n [0, 0, 0, 20, -16, 19, -8, 6, -3, -11],\n [0, 0, 0, 0, 12, -13, -10, -30, 25, 11],\n [0, 0, 0, 0, 0, 24, -5, -18, 5, -11],\n [0, 0, 0, 0, 0, 0, 23, -24, 2, 27],\n [0, 0, 0, 0, 0, 0, 0, -11, -18, 21],\n [0, 0, 0, 0, 0, 0, 0, 0, 17, 3],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
680
|
math
|
train
|
math_arithmetic_matrix_determinant_level_6_6_325
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6
|
{
"role": [
"user"
],
"content": [
"Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, 14, -2, -10, -19, -10, -10, 0, -18, -10],\n [14, -27, 12, -6, -2, 3, 3, -8, -17, -24],\n [-2, 12, 13, 19, 4, 12, 0, -18, -4, 10],\n [-10, -6, 19, -28, 20, 12, 0, -6, -6, -13],\n [-19, -2, 4, 20, -20, -10, 22, 6, 18, 18],\n [-10, 3, 12, 12, -10, -9, -3, 14, -2, -3],\n [-10, 3, 0, 0, 22, -3, -1, -18, -4, -2],\n [0, -8, -18, -6, 6, 14, -18, 10, 3, 0],\n [-18, -17, -4, -6, 18, -2, -4, 3, 16, 9],\n [-10, -24, 10, -13, 18, -3, -2, 0, 9, -28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
712
|
math
|
train
|
math_arithmetic_matrix_determinant_level_6_6_326
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6
|
{
"role": [
"user"
],
"content": [
"Compute |A| for the matrix A =\n[[-23, -2, -7, -6, -6, -7, -10, 20, -7, -21],\n [-2, 7, -6, 18, 0, -26, 2, 8, -2, 20],\n [-7, -6, 0, -2, -16, -16, 7, 6, -20, 10],\n [-6, 18, -2, 13, -4, -12, 1, 12, 10, -8],\n [-6, 0, -16, -4, 0, -1, -4, 8, 12, 14],\n [-7, -26, -16, -12, -1, -20, 18, -17, 14, -4],\n [-10, 2, 7, 1, -4, 18, -13, -21, -9, 14],\n [20, 8, 6, 12, 8, -17, -21, -29, -26, 4],\n [-7, -2, -20, 10, 12, 14, -9, -26, 2, -4],\n [-21, 20, 10, -8, 14, -4, 14, 4, -4, 22]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
198
|
math
|
train
|
math_arithmetic_matrix_determinant_level_6_6_327
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6
|
{
"role": [
"user"
],
"content": [
"What is the determinant of the matrix:\n[[-17, -4, -14, 0, 17, 0, -12, -20, -17, -3],\n [-4, -21, 16, -25, -9, 6, 11, -12, -2, -12],\n [-14, 16, -24, 16, 18, -1, -10, -8, 12, 1],\n [0, -25, 16, -24, -4, -5, 0, 16, 7, -6],\n [17, -9, 18, -4, -25, -4, -5, 4, -9, 7],\n [0, 6, -1, -5, -4, 5, -18, 6, -2, 18],\n [-12, 11, -10, 0, -5, -18, -3, -20, -6, 10],\n [-20, -12, -8, 16, 4, 6, -20, -5, 18, 14],\n [-17, -2, 12, 7, -9, -2, -6, 18, -22, -2],\n [-3, -12, 1, -6, 7, 18, 10, 14, -2, -18]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
551
|
math
|
train
|
math_arithmetic_matrix_determinant_level_6_6_328
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6
|
{
"role": [
"user"
],
"content": [
"Determine the value of det(A) where A =\n[[-26, -1, 2, 13, 10, -14, 9, 28, -19, 2],\n [0, -4, 13, -13, -12, 24, -6, -3, -1, 3],\n [0, 0, 19, -23, 8, -20, 7, -5, 21, -18],\n [0, 0, 0, -12, 7, -27, 17, -3, -13, -24],\n [0, 0, 0, 0, -29, 7, 10, 6, -15, -23],\n [0, 0, 0, 0, 0, -9, -8, 30, 2, -11],\n [0, 0, 0, 0, 0, 0, 12, 22, -23, -18],\n [0, 0, 0, 0, 0, 0, 0, -2, 11, -24],\n [0, 0, 0, 0, 0, 0, 0, 0, 28, 21],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -26]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
296
|
math
|
train
|
math_arithmetic_matrix_determinant_level_6_6_329
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6
|
{
"role": [
"user"
],
"content": [
"Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-20, 10, -14, 19, -12, -26, 13, -3, 17, 7],\n [0, -2, 13, 22, -23, -3, -8, -24, -10, -13],\n [0, 0, 28, -14, 25, -4, 25, -15, -18, 2],\n [0, 0, 0, 28, 5, 10, -15, 6, -6, 13],\n [0, 0, 0, 0, -25, 10, -24, 30, -8, 14],\n [0, 0, 0, 0, 0, -17, -12, 10, 2, -4],\n [0, 0, 0, 0, 0, 0, -29, 3, -11, 7],\n [0, 0, 0, 0, 0, 0, 0, 3, 0, 2],\n [0, 0, 0, 0, 0, 0, 0, 0, -4, -3],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0
|
math
|
train
|
math_arithmetic_matrix_determinant_level_6_6_330
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6
|
{
"role": [
"user"
],
"content": [
"Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[24, 22, 8, 6, -26, -16, -11, 13, 4, 0],\n [22, -28, -8, 2, 16, -15, -4, -14, 11, -18],\n [8, -8, 26, -20, -23, 2, 7, 20, -15, -12],\n [6, 2, -20, -12, 19, -11, -13, -11, -14, -10],\n [-26, 16, -23, 19, 6, 12, 16, -11, 24, 18],\n [-16, -15, 2, -11, 12, -26, -4, -8, 18, 13],\n [-11, -4, 7, -13, 16, -4, 22, -12, 0, 11],\n [13, -14, 20, -11, -11, -8, -12, -29, 10, -3],\n [4, 11, -15, -14, 24, 18, 0, 10, -28, 4],\n [0, -18, -12, -10, 18, 13, 11, -3, 4, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
238
|
math
|
train
|
math_arithmetic_matrix_determinant_level_6_6_331
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6
|
{
"role": [
"user"
],
"content": [
"What is the determinant of the matrix:\n[[-29, -16, 0, 0, -9, 25, 10, -11, 1, 9],\n [-16, -20, 10, 16, -16, 14, 1, 16, -4, -1],\n [0, 10, -30, -10, -10, 15, 3, -19, -1, -12],\n [0, 16, -10, -19, -2, 12, -6, 6, 0, -4],\n [-9, -16, -10, -2, 0, -8, -22, -17, 9, -2],\n [25, 14, 15, 12, -8, -8, -2, -2, 13, -12],\n [10, 1, 3, -6, -22, -2, -15, -4, 18, -15],\n [-11, 16, -19, 6, -17, -2, -4, 27, 2, -18],\n [1, -4, -1, 0, 9, 13, 18, 2, 11, -10],\n [9, -1, -12, -4, -2, -12, -15, -18, -10, -28]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
400
|
math
|
train
|
math_arithmetic_matrix_determinant_level_6_6_332
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6
|
{
"role": [
"user"
],
"content": [
"Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[20, 3, 4, -28, 6, 13, -8, 10, 23, -13],\n [3, 21, -5, -4, -14, 6, 21, 14, 1, -10],\n [4, -5, -10, -5, 6, -3, -3, 10, -3, -6],\n [-28, -4, -5, -9, -9, 6, 0, 6, 23, 12],\n [6, -14, 6, -9, 2, -4, 15, -6, -6, -10],\n [13, 6, -3, 6, -4, 2, 8, -9, 11, 12],\n [-8, 21, -3, 0, 15, 8, 1, 26, -16, -12],\n [10, 14, 10, 6, -6, -9, 26, 4, 16, -11],\n [23, 1, -3, 23, -6, 11, -16, 16, 8, -14],\n [-13, -10, -6, 12, -10, 12, -12, -11, -14, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
422
|
math
|
train
|
math_arithmetic_matrix_determinant_level_6_6_333
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6
|
{
"role": [
"user"
],
"content": [
"Compute |A| for the matrix A =\n[[18, 24, -4, 22, -20, 7, 2, -4, 8, -1],\n [24, 7, 4, -21, 20, -18, -12, 12, -15, 4],\n [-4, 4, 18, -2, -2, -1, -28, 20, 8, 18],\n [22, -21, -2, -13, 20, 2, 8, 30, -2, -10],\n [-20, 20, -2, 20, 0, -13, 2, -10, 8, -28],\n [7, -18, -1, 2, -13, -18, -10, -11, -10, -16],\n [2, -12, -28, 8, 2, -10, 17, -2, -13, 16],\n [-4, 12, 20, 30, -10, -11, -2, -19, 8, -16],\n [8, -15, 8, -2, 8, -10, -13, 8, -24, 18],\n [-1, 4, 18, -10, -28, -16, 16, -16, 18, -1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
300
|
math
|
train
|
math_arithmetic_matrix_determinant_level_6_6_334
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6
|
{
"role": [
"user"
],
"content": [
"What is the determinant of the matrix:\n[[-25, 8, -25, -18, -10, 23, -11, -19, 9, -1],\n [0, 25, -7, 3, 19, 11, 24, -24, 18, 3],\n [0, 0, -16, -24, 25, 16, -9, 28, 13, 24],\n [0, 0, 0, 18, 29, -25, 10, 15, 12, -14],\n [0, 0, 0, 0, 10, 30, -20, 14, 6, 24],\n [0, 0, 0, 0, 0, -11, -24, 0, 9, 16],\n [0, 0, 0, 0, 0, 0, -18, 20, 28, 15],\n [0, 0, 0, 0, 0, 0, 0, 22, -24, 28],\n [0, 0, 0, 0, 0, 0, 0, 0, -25, -11],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 21]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0
|
math
|
train
|
math_arithmetic_matrix_determinant_level_6_6_335
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6
|
{
"role": [
"user"
],
"content": [
"Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-10, 18, -17, 6, 6, 8, 15, -16, 20, -30],\n [0, -17, -20, -17, -1, 3, 9, 9, -10, -29],\n [0, 0, 3, 22, -23, -24, 12, 27, 11, 16],\n [0, 0, 0, 28, 6, -17, -16, -19, 28, 9],\n [0, 0, 0, 0, 20, 26, -29, -26, -6, -19],\n [0, 0, 0, 0, 0, -27, -1, 30, 28, -26],\n [0, 0, 0, 0, 0, 0, 27, 21, 20, 7],\n [0, 0, 0, 0, 0, 0, 0, 24, -26, -3],\n [0, 0, 0, 0, 0, 0, 0, 0, 23, 4],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
400
|
math
|
train
|
math_arithmetic_matrix_determinant_level_6_6_336
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6
|
{
"role": [
"user"
],
"content": [
"Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-23, -12, -12, 4, -7, -2, -6, -4, -14, 16],\n [-12, 24, 12, -21, 0, -4, -14, 0, -1, 6],\n [-12, 12, -30, -17, 24, 16, -4, 2, 4, 6],\n [4, -21, -17, 2, 12, -12, 7, -2, -18, 16],\n [-7, 0, 24, 12, -26, 6, -14, 30, -27, 6],\n [-2, -4, 16, -12, 6, 27, 0, 20, 16, -2],\n [-6, -14, -4, 7, -14, 0, 30, 0, 4, 13],\n [-4, 0, 2, -2, 30, 20, 0, 16, 2, -4],\n [-14, -1, 4, -18, -27, 16, 4, 2, 25, -8],\n [16, 6, 6, 16, 6, -2, 13, -4, -8, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
824
|
math
|
train
|
math_arithmetic_matrix_determinant_level_6_6_337
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6
|
{
"role": [
"user"
],
"content": [
"Determine the value of det(A) where A =\n[[-16, -14, 8, -22, -18, -2, -7, 6, -1, -29],\n [0, -14, 0, -1, -17, -5, 27, 28, 19, -3],\n [0, 0, 28, -19, -16, -7, -24, 19, -19, 19],\n [0, 0, 0, 28, -28, -29, 22, 1, 21, -7],\n [0, 0, 0, 0, -4, 4, -6, 4, 3, -10],\n [0, 0, 0, 0, 0, 5, 19, 13, 23, -23],\n [0, 0, 0, 0, 0, 0, 30, 10, 23, 19],\n [0, 0, 0, 0, 0, 0, 0, 4, -15, -12],\n [0, 0, 0, 0, 0, 0, 0, 0, -14, 1],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 22]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
200
|
math
|
train
|
math_arithmetic_matrix_determinant_level_6_6_338
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6
|
{
"role": [
"user"
],
"content": [
"What is the determinant of the matrix:\n[[-2, 29, 26, -22, 6, -11, 23, 15, 23, -23],\n [-28, -24, -21, 8, 22, -15, 26, 19, 19, 27],\n [29, 21, -30, -8, 8, 24, 5, -2, -22, -4],\n [9, -19, 4, -5, 7, -10, -28, 18, 14, -22],\n [4, 10, -3, 30, 0, 23, -21, -5, -22, -2],\n [-21, 13, -8, 5, -7, 5, -13, -9, 11, -18],\n [26, -21, 15, 12, -26, -20, 27, 4, 14, 27],\n [1, -30, 16, 20, 24, -18, 7, -25, -17, 20],\n [-28, -25, 27, 1, 29, 30, -20, -4, 28, 8],\n [-30, 11, 19, -4, -7, -11, 17, -4, -24, 16]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
884
|
math
|
train
|
math_arithmetic_matrix_determinant_level_6_6_339
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6
|
{
"role": [
"user"
],
"content": [
"Determine the value of det(A) where A =\n[[3, 15, -7, 20, -22, 6, -2, 13, 9, -12],\n [0, -22, 10, -8, -29, -30, -26, -19, 19, 7],\n [0, 0, -13, 24, -12, 1, 29, -26, 7, -7],\n [0, 0, 0, 16, 23, 18, 15, -1, -19, -28],\n [0, 0, 0, 0, -24, -19, -9, 18, -15, 13],\n [0, 0, 0, 0, 0, 3, -28, 19, -4, -2],\n [0, 0, 0, 0, 0, 0, -4, -8, -14, -21],\n [0, 0, 0, 0, 0, 0, 0, 3, -26, -10],\n [0, 0, 0, 0, 0, 0, 0, 0, -9, 14],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -3]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
784
|
math
|
train
|
math_arithmetic_matrix_determinant_level_6_6_340
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6
|
{
"role": [
"user"
],
"content": [
"Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[11, 24, -17, 15, 5, 25, 3, -27, -26, 19],\n [0, 14, -19, -6, -27, -21, 11, 14, 2, 5],\n [0, 0, 27, 25, -30, 28, -14, -23, 17, 22],\n [0, 0, 0, -2, 13, 10, 5, 20, 2, -13],\n [0, 0, 0, 0, 16, -7, -15, -30, 27, -20],\n [0, 0, 0, 0, 0, -16, -26, 1, -1, 23],\n [0, 0, 0, 0, 0, 0, -23, 9, 7, 22],\n [0, 0, 0, 0, 0, 0, 0, 28, 27, -28],\n [0, 0, 0, 0, 0, 0, 0, 0, 18, -28],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
408
|
math
|
train
|
math_arithmetic_matrix_determinant_level_6_6_341
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6
|
{
"role": [
"user"
],
"content": [
"What is the determinant of the matrix:\n[[-25, -27, 21, -29, -2, -7, 8, -17, -16, -5],\n [6, -2, 27, 12, -9, 6, 5, 5, -19, -15],\n [-17, -1, 28, -19, 1, 11, 6, -11, 29, -15],\n [6, 26, 27, 8, -1, 25, -30, 13, 2, 5],\n [19, 24, 10, -16, 11, 3, -16, -29, -10, 3],\n [25, -23, 18, 13, 16, 20, -24, -28, 14, -22],\n [13, 16, -26, 13, 11, 25, 16, -25, -9, 5],\n [9, -28, -16, 17, 12, 30, 19, 28, -22, -20],\n [2, 10, -26, 2, 19, -18, -30, -23, 11, -22],\n [-10, -16, 10, 6, -29, 22, 9, -25, 3, -24]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
916
|
math
|
train
|
math_arithmetic_matrix_determinant_level_6_6_342
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6
|
{
"role": [
"user"
],
"content": [
"What is the determinant of the matrix:\n[[28, 4, -6, 9, 28, -15, 17, -24, -14, 13],\n [21, 25, -20, 25, -22, -25, -27, -15, -15, 7],\n [13, -17, 27, -6, -4, 5, -7, 11, 10, -14],\n [-20, 30, -18, -13, 6, 22, -24, 23, 3, -4],\n [-20, -26, -3, -8, -7, 19, -4, 11, -25, -20],\n [-19, -11, -10, 29, 29, -21, -29, 27, 14, -7],\n [-26, -4, -27, 7, -22, -15, -12, -10, 1, -16],\n [18, -6, 4, -25, -3, -21, -20, -30, 14, 8],\n [-18, 14, 6, 16, -10, -10, 26, -2, -15, 6],\n [22, 4, -9, -27, -19, 18, -5, 13, 10, -12]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
341
|
math
|
train
|
math_arithmetic_matrix_determinant_level_6_6_343
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6
|
{
"role": [
"user"
],
"content": [
"Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-24, -18, 18, 9, 22, -13, -4, -20, -18, 28],\n [23, -1, 30, -15, -14, 14, 29, -7, 11, 7],\n [2, -8, -21, -11, 15, -11, 22, 29, 7, -17],\n [28, -18, -5, 13, 5, 6, -10, 8, -15, 29],\n [6, -1, -15, -14, 27, 15, -7, 29, 5, 7],\n [-13, -10, -23, 28, -23, 3, 28, 11, 25, -16],\n [-22, 21, 10, -8, 16, -29, 11, 18, 11, 4],\n [-5, -19, 1, -28, -7, 14, -8, 2, 5, 3],\n [-2, -14, 17, 28, 12, 20, -20, -13, 8, 28],\n [24, 14, -30, 1, -25, -30, 3, -28, -8, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
293
|
math
|
train
|
math_arithmetic_matrix_determinant_level_6_6_344
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6
|
{
"role": [
"user"
],
"content": [
"What is the determinant of the matrix:\n[[24, -4, -8, 8, 4, 6, 1, -16, -22, 21],\n [-4, -27, 8, 16, 12, 0, 16, 10, 3, 8],\n [-8, 8, 9, -18, -4, 0, 14, -10, 12, 12],\n [8, 16, -18, 16, 6, -24, -13, -4, -12, 6],\n [4, 12, -4, 6, -17, 17, -16, -16, 4, 12],\n [6, 0, 0, -24, 17, 26, -20, 0, 14, 1],\n [1, 16, 14, -13, -16, -20, -10, 10, 4, -6],\n [-16, 10, -10, -4, -16, 0, 10, 28, -11, 20],\n [-22, 3, 12, -12, 4, 14, 4, -11, 26, 9],\n [21, 8, 12, 6, 12, 1, -6, 20, 9, 0]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
580
|
math
|
train
|
math_arithmetic_matrix_determinant_level_6_6_345
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6
|
{
"role": [
"user"
],
"content": [
"Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-30, 4, 8, 0, -26, -12, 18, 16, 5, -16],\n [4, 20, 4, 16, -4, 5, 9, 8, -10, 0],\n [8, 4, -30, -4, -22, -2, 9, -28, -6, -2],\n [0, 16, -4, -20, -16, 6, -8, -8, -4, 18],\n [-26, -4, -22, -16, 29, -2, -16, 18, 3, -4],\n [-12, 5, -2, 6, -2, -25, -2, -6, 27, -20],\n [18, 9, 9, -8, -16, -2, 8, 3, -20, -20],\n [16, 8, -28, -8, 18, -6, 3, 25, 12, 6],\n [5, -10, -6, -4, 3, 27, -20, 12, -3, -14],\n [-16, 0, -2, 18, -4, -20, -20, 6, -14, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
415
|
math
|
train
|
math_arithmetic_matrix_determinant_level_6_6_346
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6
|
{
"role": [
"user"
],
"content": [
"Compute |A| for the matrix A =\n[[-13, 0, 24, 3, 5, -21, -2, -6, 9, 8],\n [0, -21, 25, -14, 18, 0, -22, 6, 6, 19],\n [24, 25, 10, -6, -16, 9, -4, -2, -10, 2],\n [3, -14, -6, -30, 7, -18, -14, 15, -13, -2],\n [5, 18, -16, 7, 16, 8, 4, 5, -4, 16],\n [-21, 0, 9, -18, 8, -22, -6, 12, -4, -6],\n [-2, -22, -4, -14, 4, -6, 9, 16, 3, 12],\n [-6, 6, -2, 15, 5, 12, 16, -9, 6, -5],\n [9, 6, -10, -13, -4, -4, 3, 6, 28, -10],\n [8, 19, 2, -2, 16, -6, 12, -5, -10, -23]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
16
|
math
|
train
|
math_arithmetic_matrix_determinant_level_6_6_347
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6
|
{
"role": [
"user"
],
"content": [
"What is the determinant of the matrix:\n[[-22, -2, -12, 2, 26, 12, 13, -9, 17, 6],\n [-2, 8, -26, -20, -6, -14, 6, -14, -8, -12],\n [-12, -26, 8, 26, -14, -17, 9, -18, -24, -4],\n [2, -20, 26, 11, -24, -14, -22, -12, -3, -20],\n [26, -6, -14, -24, 29, -16, 23, -18, 6, 15],\n [12, -14, -17, -14, -16, 30, -8, 24, -6, 8],\n [13, 6, 9, -22, 23, -8, -1, -14, -18, 14],\n [-9, -14, -18, -12, -18, 24, -14, -11, 1, 3],\n [17, -8, -24, -3, 6, -6, -18, 1, 16, -3],\n [6, -12, -4, -20, 15, 8, 14, 3, -3, -15]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
767
|
math
|
train
|
math_arithmetic_matrix_determinant_level_6_6_348
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6
|
{
"role": [
"user"
],
"content": [
"What is the determinant of the matrix:\n[[29, -1, -2, 8, 0, -22, -4, -4, 22, 6],\n [-1, 27, -4, -2, 0, -4, 20, -24, -14, -16],\n [-2, -4, 6, -24, -1, -14, -2, -6, 0, -22],\n [8, -2, -24, 20, -16, -20, -19, -14, 1, -22],\n [0, 0, -1, -16, 19, -12, -4, 7, 2, 3],\n [-22, -4, -14, -20, -12, -19, 0, 8, 2, 19],\n [-4, 20, -2, -19, -4, 0, 5, -16, -25, -22],\n [-4, -24, -6, -14, 7, 8, -16, -23, 24, 12],\n [22, -14, 0, 1, 2, 2, -25, 24, -30, -11],\n [6, -16, -22, -22, 3, 19, -22, 12, -11, 13]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
52
|
math
|
train
|
math_arithmetic_matrix_determinant_level_6_6_349
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6
|
{
"role": [
"user"
],
"content": [
"Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, -8, -7, 22, 21, 4, -3, 6, -8, -12],\n [-8, -23, -12, 9, 16, -16, -7, 4, 10, 4],\n [-7, -12, -22, 8, 0, -3, 4, 16, 30, 3],\n [22, 9, 8, 17, 0, -20, 4, -1, 8, 2],\n [21, 16, 0, 0, 23, 16, -14, -6, 8, 8],\n [4, -16, -3, -20, 16, 18, 22, 12, 10, 2],\n [-3, -7, 4, 4, -14, 22, -23, 26, 16, -14],\n [6, 4, 16, -1, -6, 12, 26, -22, -1, -16],\n [-8, 10, 30, 8, 8, 10, 16, -1, -27, -2],\n [-12, 4, 3, 2, 8, 2, -14, -16, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
914
|
math
|
train
|
math_arithmetic_matrix_determinant_level_6_6_350
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6
|
{
"role": [
"user"
],
"content": [
"Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[20, -6, -8, 7, -7, -10, -12, 24, -8, 12],\n [-6, -27, -16, -2, 6, 0, -14, -18, 12, -8],\n [-8, -16, -9, 6, 11, 16, 4, -2, -14, 8],\n [7, -2, 6, -17, 8, -10, -26, -2, -4, 3],\n [-7, 6, 11, 8, -29, -2, -4, 13, 12, -22],\n [-10, 0, 16, -10, -2, 15, 14, -6, 22, -2],\n [-12, -14, 4, -26, -4, 14, 3, 22, 14, -3],\n [24, -18, -2, -2, 13, -6, 22, -7, 9, 4],\n [-8, 12, -14, -4, 12, 22, 14, 9, 26, -15],\n [12, -8, 8, 3, -22, -2, -3, 4, -15, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
779
|
math
|
train
|
math_arithmetic_matrix_determinant_level_6_6_351
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6
|
{
"role": [
"user"
],
"content": [
"Determine the value of det(A) where A =\n[[27, -6, 8, 26, -29, 1, 8, 14, -26, -10],\n [0, -14, 25, -12, 27, -7, 19, -29, -19, -19],\n [0, 0, 10, 16, 21, -20, -11, -15, -30, -22],\n [0, 0, 0, 24, 28, -22, 10, -18, 6, 9],\n [0, 0, 0, 0, 25, 10, 13, -10, -18, -8],\n [0, 0, 0, 0, 0, -23, 27, -15, -21, 14],\n [0, 0, 0, 0, 0, 0, -28, 11, 7, -24],\n [0, 0, 0, 0, 0, 0, 0, -21, 6, -26],\n [0, 0, 0, 0, 0, 0, 0, 0, -17, 10],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 21]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0
|
math
|
train
|
math_arithmetic_matrix_determinant_level_6_6_352
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6
|
{
"role": [
"user"
],
"content": [
"Compute |A| for the matrix A =\n[[28, -18, -7, 7, -29, -8, -30, -16, 27, -23],\n [-28, 20, -5, -5, -23, 13, 21, 19, 8, 9],\n [4, -20, 17, -24, -27, 18, 11, -12, 20, 28],\n [13, 21, 25, 13, -15, 7, 27, 9, -4, -15],\n [10, -30, -25, 27, 27, 25, -30, -3, 12, 26],\n [14, -14, 0, -8, -11, 21, -25, 19, 0, -3],\n [-13, 18, 29, -25, -21, -28, -3, -28, 27, 20],\n [-28, 6, -14, -28, 11, 11, -8, -23, 3, 10],\n [19, -13, 30, 6, -5, 28, 24, -10, -25, -9],\n [0, -24, 16, 13, -26, -2, 2, 13, -27, 2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
482
|
math
|
train
|
math_arithmetic_matrix_determinant_level_6_6_353
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6
|
{
"role": [
"user"
],
"content": [
"Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, -15, -16, 25, 7, -3, 17, -7, 17, -24],\n [11, -25, 13, 24, 19, 16, -29, 25, 11, 8],\n [-24, 22, 2, 11, -26, 22, 25, 28, 10, -5],\n [24, 14, -21, -9, -2, -2, -5, 3, 1, -2],\n [11, 24, 25, 12, -13, -21, 6, -10, -19, -24],\n [-17, 2, -15, -26, 16, -20, -13, 26, 27, -3],\n [28, -8, -6, -26, 23, -20, 18, -16, -24, -9],\n [-27, -26, 7, 27, 22, -24, -20, 23, 10, 15],\n [-21, -23, 10, -20, 9, -3, 17, 19, 19, -15],\n [16, 12, 23, -5, -18, -29, 10, -15, 5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
216
|
math
|
train
|
math_arithmetic_matrix_determinant_level_6_6_354
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6
|
{
"role": [
"user"
],
"content": [
"Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-19, 16, -7, 8, 24, -27, 27, 0, -11, -25],\n [0, 19, -16, -7, -8, -22, -28, -19, -6, 21],\n [0, 0, 8, -1, 27, -20, -27, 8, -9, 26],\n [0, 0, 0, -4, 21, 24, -27, 26, -9, 14],\n [0, 0, 0, 0, 6, 4, -26, -7, 30, -8],\n [0, 0, 0, 0, 0, 13, -29, -9, -29, 10],\n [0, 0, 0, 0, 0, 0, 21, 18, -11, 2],\n [0, 0, 0, 0, 0, 0, 0, -21, 6, -19],\n [0, 0, 0, 0, 0, 0, 0, 0, 24, 3],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
264
|
math
|
train
|
math_arithmetic_matrix_determinant_level_6_6_355
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6
|
{
"role": [
"user"
],
"content": [
"Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[29, 13, 13, -18, -9, 17, -29, -27, -12, 11],\n [8, -29, -30, -22, -11, 25, -6, -11, -21, -3],\n [27, -29, 4, 15, 7, -20, -19, 23, -3, 2],\n [3, -8, -18, -3, -29, -4, -2, 21, 4, -29],\n [27, -28, 27, 12, 10, 16, -12, -29, -30, 17],\n [30, 15, -2, -28, -20, 22, -15, 11, 26, 25],\n [2, -26, -27, -2, -24, -18, -12, 8, 0, -15],\n [13, 3, 6, -5, -25, -12, -2, 15, -28, 26],\n [-13, 28, 16, -30, -28, -10, -20, 0, 22, 25],\n [-10, 26, 24, -25, -25, 2, 14, 0, -15, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
197
|
math
|
train
|
math_arithmetic_matrix_determinant_level_6_6_356
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6
|
{
"role": [
"user"
],
"content": [
"Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[24, 4, -7, 24, -28, 29, -7, -7, -11, -6],\n [4, -30, -15, 18, 5, -21, -23, 26, 25, -24],\n [26, 20, 14, 14, -30, 15, -11, 19, 26, -5],\n [1, -26, 21, -8, -9, -30, -29, -20, -25, -19],\n [5, 4, -23, -14, -6, 15, -25, 12, -10, 28],\n [-4, -23, 12, 17, -15, 10, -28, -22, 19, -20],\n [26, -29, 23, -22, -3, 5, -12, 21, -7, 6],\n [-4, -11, 9, -1, -8, -10, -23, 3, 18, -27],\n [9, 0, -23, 21, -19, 28, -6, -25, 19, 9],\n [0, 1, -27, 7, 29, 18, -18, -8, 30, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
746
|
math
|
train
|
math_arithmetic_matrix_determinant_level_6_6_357
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6
|
{
"role": [
"user"
],
"content": [
"Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-13, -4, 25, 18, -20, 4, -10, -2, 18, -9],\n [0, 11, 0, -8, 3, -25, -5, -30, -27, -26],\n [0, 0, -8, 29, -10, -11, 17, -7, 18, 26],\n [0, 0, 0, -21, -9, -8, -21, -1, 18, 0],\n [0, 0, 0, 0, 18, -29, -15, -27, -30, -16],\n [0, 0, 0, 0, 0, 19, 15, -14, 6, 23],\n [0, 0, 0, 0, 0, 0, 28, 20, 30, -15],\n [0, 0, 0, 0, 0, 0, 0, 27, -9, -5],\n [0, 0, 0, 0, 0, 0, 0, 0, 8, 5],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
840
|
math
|
train
|
math_arithmetic_matrix_determinant_level_6_6_358
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6
|
{
"role": [
"user"
],
"content": [
"Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-16, 2, 23, 11, -25, -15, -18, 26, 16, 6],\n [-13, -24, -8, -16, -1, 21, 30, 25, -25, -19],\n [-4, -3, -6, 14, 22, 25, -17, 4, 28, -12],\n [-8, 14, -13, -28, -14, -4, 9, -12, 11, 0],\n [22, 4, 15, -20, 0, 27, 17, 10, 16, 16],\n [-19, -14, 8, 22, -8, -16, 13, -15, 11, -11],\n [4, 0, 27, 29, 3, -30, -13, 13, -22, -30],\n [18, 29, 11, -3, 17, -24, 4, -18, 20, -26],\n [-5, 17, 16, -22, 20, 17, 15, -24, 0, 25],\n [-15, -25, 25, 9, 6, -6, 6, -14, 13, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
967
|
math
|
train
|
math_arithmetic_matrix_determinant_level_6_6_359
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6
|
{
"role": [
"user"
],
"content": [
"Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-20, 18, 0, -16, 16, -7, -16, 8, -5, 25],\n [18, 25, 2, -17, 2, 14, 7, 0, 0, -12],\n [0, 2, 22, 29, 10, -21, 5, 2, -14, -3],\n [-16, -17, 29, 4, -14, -12, 14, -1, -6, -16],\n [16, 2, 10, -14, -29, -23, 4, 13, 12, -3],\n [-7, 14, -21, -12, -23, 1, 6, 0, 0, -19],\n [-16, 7, 5, 14, 4, 6, 25, 10, -4, -2],\n [8, 0, 2, -1, 13, 0, 10, 16, 30, 19],\n [-5, 0, -14, -6, 12, 0, -4, 30, -11, 2],\n [25, -12, -3, -16, -3, -19, -2, 19, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
529
|
math
|
train
|
math_arithmetic_matrix_determinant_level_6_6_360
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6
|
{
"role": [
"user"
],
"content": [
"Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-21, 4, -8, 5, 28, -3, -13, 26, 12, 23],\n [0, 13, 29, -9, -22, -21, -30, 26, -12, 9],\n [0, 0, -1, -14, -28, 23, 18, -27, 8, 10],\n [0, 0, 0, 12, -30, 1, -14, 24, -3, 1],\n [0, 0, 0, 0, 3, -11, -18, 5, 17, -20],\n [0, 0, 0, 0, 0, -15, 3, -8, 1, -8],\n [0, 0, 0, 0, 0, 0, 24, -6, -8, -15],\n [0, 0, 0, 0, 0, 0, 0, -21, -25, 30],\n [0, 0, 0, 0, 0, 0, 0, 0, -9, -6],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
880
|
math
|
train
|
math_arithmetic_matrix_determinant_level_6_6_361
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6
|
{
"role": [
"user"
],
"content": [
"Compute |A| for the matrix A =\n[[30, 25, 1, 4, 6, 2, 10, 8, -15, 14],\n [25, -7, -16, -4, 7, 20, 8, -16, -15, -20],\n [1, -16, 9, 14, -22, 5, -16, 10, 0, 6],\n [4, -4, 14, 13, 1, -20, 8, -16, 22, -25],\n [6, 7, -22, 1, 30, -4, 11, -2, 14, 17],\n [2, 20, 5, -20, -4, -5, 23, 3, -4, 2],\n [10, 8, -16, 8, 11, 23, 5, -12, 10, -12],\n [8, -16, 10, -16, -2, 3, -12, 2, 12, 18],\n [-15, -15, 0, 22, 14, -4, 10, 12, 9, 4],\n [14, -20, 6, -25, 17, 2, -12, 18, 4, -29]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
112
|
math
|
train
|
math_arithmetic_matrix_determinant_level_6_6_362
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6
|
{
"role": [
"user"
],
"content": [
"Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[25, 8, 21, 0, 3, -2, 2, -8, 17, -18],\n [8, -1, -4, 2, -14, 12, -22, -12, -8, -2],\n [21, -4, -13, -11, -2, -9, -6, -22, -18, 20],\n [0, 2, -11, 21, 29, 13, 6, 4, 8, 17],\n [3, -14, -2, 29, -28, -10, -4, -2, -16, -17],\n [-2, 12, -9, 13, -10, 23, -20, -10, 12, 4],\n [2, -22, -6, 6, -4, -20, -11, -1, -3, 10],\n [-8, -12, -22, 4, -2, -10, -1, -28, 20, -24],\n [17, -8, -18, 8, -16, 12, -3, 20, -3, 2],\n [-18, -2, 20, 17, -17, 4, 10, -24, 2, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
138
|
math
|
train
|
math_arithmetic_matrix_determinant_level_6_6_363
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6
|
{
"role": [
"user"
],
"content": [
"Determine the value of det(A) where A =\n[[27, 4, 11, -1, -26, 25, 14, 0, -2, 1],\n [0, 26, -3, 13, -25, 10, -2, -28, 29, 11],\n [0, 0, -27, -9, 6, -21, 10, 10, 18, -20],\n [0, 0, 0, -4, 14, 10, -22, 8, 16, -24],\n [0, 0, 0, 0, -7, 10, 10, 19, 8, -2],\n [0, 0, 0, 0, 0, 10, -2, 9, -26, 9],\n [0, 0, 0, 0, 0, 0, 29, -19, 18, -1],\n [0, 0, 0, 0, 0, 0, 0, -11, -20, 18],\n [0, 0, 0, 0, 0, 0, 0, 0, -8, 30],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 26]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
760
|
math
|
train
|
math_arithmetic_matrix_determinant_level_6_6_364
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6
|
{
"role": [
"user"
],
"content": [
"Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[28, 24, 16, -4, -23, 25, 20, -17, 5, 30],\n [0, 10, -17, 9, 30, -2, -14, 6, 14, -2],\n [0, 0, 29, 30, -19, -3, -6, -19, -20, -13],\n [0, 0, 0, -26, -22, 15, -12, 24, 27, -25],\n [0, 0, 0, 0, 9, 29, -11, 11, -30, 16],\n [0, 0, 0, 0, 0, 29, -24, -15, 15, -26],\n [0, 0, 0, 0, 0, 0, -3, 8, -5, -9],\n [0, 0, 0, 0, 0, 0, 0, -13, -18, -23],\n [0, 0, 0, 0, 0, 0, 0, 0, 30, -14],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0
|
math
|
train
|
math_arithmetic_matrix_determinant_level_6_6_365
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6
|
{
"role": [
"user"
],
"content": [
"Compute |A| for the matrix A =\n[[7, 27, -10, 19, -24, -15, -24, -27, 0, -2],\n [3, -20, 18, 14, -28, 25, 30, 1, 27, -17],\n [-25, 24, -7, 10, -29, -23, -11, 7, -14, -29],\n [-4, -18, -28, -8, -10, 4, -30, -26, -12, -20],\n [-17, 28, -25, 13, 15, 30, 14, 25, 12, 8],\n [-1, -17, -11, 7, 13, 16, 25, 20, 5, -14],\n [-24, -20, 22, 20, -23, -19, -5, 14, -18, -16],\n [22, -20, 4, -30, 8, -22, -19, 20, 9, 30],\n [-11, -4, 15, -23, -25, -13, -17, 7, -5, -12],\n [-10, -9, 27, 11, 24, -27, -17, -20, 22, 14]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
221
|
math
|
train
|
math_arithmetic_matrix_determinant_level_6_6_366
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6
|
{
"role": [
"user"
],
"content": [
"Determine the value of det(A) where A =\n[[-2, 13, 30, -16, 24, -13, 24, -20, 20, -11],\n [11, 26, 12, -25, -22, -9, 22, 7, 9, 29],\n [22, 26, 22, 25, -7, 6, 21, 22, -28, 16],\n [23, 16, -29, 28, -6, -13, -20, -9, 24, -11],\n [2, -9, 18, -10, 6, -22, 27, -9, 27, -21],\n [10, 22, 9, 29, 1, -11, 30, -8, -12, 29],\n [9, -27, -6, -27, -1, 23, 1, 18, 11, 15],\n [-1, 24, -4, -20, 10, -1, 12, -28, -10, 13],\n [11, -1, 8, -5, 17, -10, -9, -7, -28, -25],\n [4, 19, -11, -7, 2, 26, -19, -13, -15, 9]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
447
|
math
|
train
|
math_arithmetic_matrix_determinant_level_6_6_367
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6
|
{
"role": [
"user"
],
"content": [
"Compute |A| for the matrix A =\n[[18, -16, 6, 14, -23, -15, -11, -9, -20, -19],\n [-27, 0, -19, 27, 3, 30, 0, -7, -16, -4],\n [0, 12, -22, -4, 0, -28, 1, -24, 8, -30],\n [-21, 12, 18, 13, -12, -8, 27, 6, 23, -23],\n [26, -14, 19, 22, 8, 20, -2, -25, -3, 26],\n [-25, 14, -4, 15, 2, -2, -18, 23, 20, -3],\n [0, 15, -9, 18, 1, 12, -9, -7, 20, 5],\n [11, -27, -7, 10, -5, 17, 0, 29, 16, 0],\n [-30, 5, -19, 30, -9, -16, 6, -12, -14, -4],\n [-9, 2, -23, 30, -28, 23, -15, 19, 19, 1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
995
|
math
|
train
|
math_arithmetic_matrix_determinant_level_6_6_368
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6
|
{
"role": [
"user"
],
"content": [
"What is the determinant of the matrix:\n[[13, -25, 5, 20, 24, -15, 23, -23, 29, -5],\n [0, 18, 1, 12, 6, 21, 8, -9, 20, -15],\n [0, 0, 11, 1, 17, 13, -1, 14, -5, -26],\n [0, 0, 0, 16, 18, 26, -20, 30, -27, -11],\n [0, 0, 0, 0, 21, -26, 2, -5, -13, 23],\n [0, 0, 0, 0, 0, 20, 29, -17, 0, 9],\n [0, 0, 0, 0, 0, 0, 20, 2, 6, 29],\n [0, 0, 0, 0, 0, 0, 0, 2, 0, -18],\n [0, 0, 0, 0, 0, 0, 0, 0, -6, -3],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
600
|
math
|
train
|
math_arithmetic_matrix_determinant_level_6_6_369
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6
|
{
"role": [
"user"
],
"content": [
"Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-30, 8, -27, 24, 8, 2, -2, -14, 12, 14],\n [8, -17, 14, 26, -27, -16, 0, -18, -8, -10],\n [-27, 14, 12, 2, -18, -10, 0, 21, 10, 8],\n [24, 26, 2, -22, -8, 15, 26, 10, -6, -6],\n [8, -27, -18, -8, 16, -12, -14, -7, 18, 10],\n [2, -16, -10, 15, -12, 11, 16, -3, -14, 10],\n [-2, 0, 0, 26, -14, 16, 3, 6, -10, 0],\n [-14, -18, 21, 10, -7, -3, 6, -18, -23, 16],\n [12, -8, 10, -6, 18, -14, -10, -23, 3, 7],\n [14, -10, 8, -6, 10, 10, 0, 16, 7, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
813
|
math
|
train
|
math_arithmetic_matrix_determinant_level_6_6_370
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6
|
{
"role": [
"user"
],
"content": [
"Determine the value of det(A) where A =\n[[-20, -9, -17, 21, -6, -28, 20, -18, -14, -17],\n [7, -1, 0, -18, -21, -23, 9, 29, -25, 19],\n [4, -12, 8, 20, -30, 14, 28, -2, -28, -1],\n [19, 15, 30, 13, -1, 16, 22, -30, -24, 14],\n [30, -7, -21, -27, -16, -28, -15, 2, -22, -29],\n [-26, -12, 8, -27, 8, 18, -29, -15, 9, 0],\n [22, 8, -28, 22, -8, 21, -22, -5, 7, 1],\n [-28, 7, -17, 5, -15, -2, 24, 10, 19, -21],\n [-25, 1, 8, 9, -22, -22, -16, 12, -21, 11],\n [2, -28, 8, -10, 12, 25, 25, 17, -8, 21]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
586
|
math
|
train
|
math_arithmetic_matrix_determinant_level_6_6_371
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6
|
{
"role": [
"user"
],
"content": [
"Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, 21, 1, 0, 23, 25, 10, 22, 29, 22],\n [0, 21, 18, 19, -6, -1, 10, -1, 12, -15],\n [0, 0, 2, -21, 5, -12, -20, 15, -11, -9],\n [0, 0, 0, 24, 27, -7, -22, 8, -8, -29],\n [0, 0, 0, 0, 10, -14, 12, 19, -21, -17],\n [0, 0, 0, 0, 0, 21, -12, 3, -10, -7],\n [0, 0, 0, 0, 0, 0, -14, -24, 27, 15],\n [0, 0, 0, 0, 0, 0, 0, -30, 6, -18],\n [0, 0, 0, 0, 0, 0, 0, 0, -16, 28],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
400
|
math
|
train
|
math_arithmetic_matrix_determinant_level_6_6_372
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6
|
{
"role": [
"user"
],
"content": [
"Compute |A| for the matrix A =\n[[22, 11, -2, 23, 29, 8, -30, 16, 27, -13],\n [-22, -28, -16, -20, -26, 28, -18, 8, -28, -1],\n [6, -9, 8, 14, 27, -25, 16, -20, 11, 14],\n [8, -18, -22, -19, -9, -3, -5, 1, 23, 1],\n [-8, 9, 13, -22, -7, 15, -26, 2, 7, -12],\n [-1, -15, 24, 22, -1, -11, 2, -29, 10, 4],\n [-27, 28, -19, 26, 19, 26, 12, -13, -24, 20],\n [23, 12, 8, -18, 26, -15, 28, -23, 27, 11],\n [13, -20, 26, 1, 17, 10, -15, 2, 5, 29],\n [-5, -20, -21, 5, -18, 26, 18, -1, 24, -10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
751
|
math
|
train
|
math_arithmetic_matrix_determinant_level_6_6_373
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6
|
{
"role": [
"user"
],
"content": [
"Determine the value of det(A) where A =\n[[-29, 0, 17, 26, 12, 16, 19, 26, -13, -22],\n [0, 16, -20, -23, 27, 2, -11, -19, 23, 25],\n [0, 0, -12, 28, -27, -30, -26, -6, -20, 1],\n [0, 0, 0, -3, -28, 0, -17, 30, -29, -12],\n [0, 0, 0, 0, 30, 6, -25, -18, 3, -28],\n [0, 0, 0, 0, 0, 13, 13, -13, -12, -11],\n [0, 0, 0, 0, 0, 0, 20, 23, 0, 0],\n [0, 0, 0, 0, 0, 0, 0, -22, 27, 25],\n [0, 0, 0, 0, 0, 0, 0, 0, 25, -13],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -4]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0
|
math
|
train
|
math_arithmetic_matrix_determinant_level_6_6_374
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6
|
{
"role": [
"user"
],
"content": [
"Determine the value of det(A) where A =\n[[6, -20, 2, -12, 15, 6, 19, -4, 26, 12],\n [6, 15, -8, 3, -29, 19, 2, -3, -30, -21],\n [26, 11, 0, 3, 14, 20, -4, -19, -27, -7],\n [22, 8, -16, -9, 7, -10, 1, -2, -9, 28],\n [-9, -11, -9, -17, -3, 2, -29, 5, -15, 13],\n [-11, 17, -13, -18, 2, 18, 11, 9, -6, 20],\n [-24, 16, -21, -12, 30, 26, -20, -9, 1, 25],\n [-22, 6, -13, -24, 28, 13, 0, 1, -8, -25],\n [-29, -17, 23, 30, 4, -27, 13, -22, -20, 3],\n [15, -29, -19, 21, 7, 23, -9, -18, 13, -15]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
406
|
math
|
train
|
math_arithmetic_matrix_determinant_level_6_6_375
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6
|
{
"role": [
"user"
],
"content": [
"Compute |A| for the matrix A =\n[[21, 1, 15, 30, 20, 14, -4, 4, -30, 26],\n [-17, 18, -1, 13, -21, -15, 0, 9, 27, -12],\n [27, -13, -19, 12, -6, 1, 10, -14, -22, 3],\n [-2, 24, 29, 26, -10, -24, -28, -16, 20, -12],\n [20, 30, 24, -8, 18, 23, 9, 14, 15, 27],\n [6, -30, 16, 25, -10, 7, 24, 20, 4, -4],\n [5, 10, -17, -4, -4, -16, 6, 25, 8, 28],\n [5, -9, -21, 23, -29, 16, -16, -12, -14, 3],\n [5, -3, 11, 21, -7, 18, 1, 20, -19, 12],\n [9, -7, -5, 16, 9, 30, -11, 30, 19, -4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
252
|
math
|
train
|
math_arithmetic_matrix_determinant_level_6_6_376
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6
|
{
"role": [
"user"
],
"content": [
"What is the determinant of the matrix:\n[[-7, 6, 21, -30, 8, 1, 15, 7, -8, -24],\n [0, 25, 18, -19, -16, 27, -15, 6, 5, -22],\n [0, 0, -22, 18, 4, 29, -13, -7, 3, 24],\n [0, 0, 0, -30, -1, 22, -12, 28, 10, -17],\n [0, 0, 0, 0, 12, -7, 9, -19, -21, -5],\n [0, 0, 0, 0, 0, -18, 4, -6, 24, 26],\n [0, 0, 0, 0, 0, 0, -18, 7, 27, 22],\n [0, 0, 0, 0, 0, 0, 0, 2, -16, -18],\n [0, 0, 0, 0, 0, 0, 0, 0, 13, 8],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 23]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0
|
math
|
train
|
math_arithmetic_matrix_determinant_level_6_6_377
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6
|
{
"role": [
"user"
],
"content": [
"Compute |A| for the matrix A =\n[[30, 7, -27, -21, -25, 21, -3, -15, 28, 22],\n [0, -26, 18, 0, -2, 5, 27, -24, 12, -9],\n [0, 0, 9, -19, -26, 26, -6, -9, 13, -24],\n [0, 0, 0, -16, 17, -10, -30, -19, 8, 16],\n [0, 0, 0, 0, 24, -27, 3, -3, -7, -18],\n [0, 0, 0, 0, 0, -11, -8, -27, -16, -22],\n [0, 0, 0, 0, 0, 0, 5, 26, 12, -25],\n [0, 0, 0, 0, 0, 0, 0, 9, -20, 26],\n [0, 0, 0, 0, 0, 0, 0, 0, -4, -24],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -18]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
800
|
math
|
train
|
math_arithmetic_matrix_determinant_level_6_6_378
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6
|
{
"role": [
"user"
],
"content": [
"Determine the value of det(A) where A =\n[[15, -13, 28, -14, 7, -7, -24, -25, -3, 28],\n [16, -1, 30, 23, -6, -27, -27, -17, -1, -9],\n [-10, 25, 27, 29, 2, 22, -23, -25, 14, 30],\n [-21, 28, 21, -25, 26, 0, 18, 5, 18, -20],\n [12, -4, -11, -24, -8, 22, 27, 13, -4, 10],\n [22, 7, 20, 8, 16, 26, -12, -12, -27, -30],\n [-29, -22, 17, 10, -20, 0, 6, 18, -2, -7],\n [-15, 1, 29, 15, 24, -17, 17, -27, 12, -9],\n [29, 7, -6, -27, 11, -18, 7, -18, -10, -12],\n [0, 13, 17, -15, -30, 12, 26, 20, -16, -3]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
88
|
math
|
train
|
math_arithmetic_matrix_determinant_level_6_6_379
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6
|
{
"role": [
"user"
],
"content": [
"Compute |A| for the matrix A =\n[[6, 15, -22, 8, 12, -19, 6, 26, -15, -16],\n [0, -1, 7, -19, 21, 24, 26, -4, 22, 8],\n [0, 0, 7, -6, -19, 30, 11, 26, -1, 19],\n [0, 0, 0, -5, -19, -25, 12, -24, -1, 14],\n [0, 0, 0, 0, -7, 10, 7, -3, 0, -6],\n [0, 0, 0, 0, 0, -26, -21, -30, -26, -7],\n [0, 0, 0, 0, 0, 0, -7, -7, 19, -24],\n [0, 0, 0, 0, 0, 0, 0, 23, -28, 6],\n [0, 0, 0, 0, 0, 0, 0, 0, 29, -22],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 29]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
780
|
math
|
train
|
math_arithmetic_matrix_determinant_level_6_6_380
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6
|
{
"role": [
"user"
],
"content": [
"What is the determinant of the matrix:\n[[-25, 11, 15, -18, -18, 29, 2, -6, -24, -9],\n [13, 30, 0, 17, -4, -25, 10, 3, 13, -9],\n [15, -7, -17, -27, -15, -13, 10, -18, -5, 16],\n [2, 15, -28, 30, 2, 21, 6, -27, 9, 9],\n [-28, 14, -1, -19, 23, -26, 7, -11, -7, -24],\n [9, -20, 13, -10, 14, -20, 19, -25, -15, 0],\n [-9, -29, -22, -16, 5, 22, 23, 3, 27, 28],\n [-8, -10, 4, -13, -23, -4, -5, -1, -27, -13],\n [6, -1, 8, -28, 10, 1, 13, 15, -12, 27],\n [-14, 25, 21, -25, -7, 3, -18, -22, -17, 29]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
800
|
math
|
train
|
math_arithmetic_matrix_determinant_level_6_6_381
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6
|
{
"role": [
"user"
],
"content": [
"Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[18, 19, -6, 14, -6, -7, -2, -12, 0, 16],\n [19, 22, 2, 8, 1, -15, 2, 25, -6, -12],\n [-6, 2, 13, 22, -18, 11, -16, -8, -14, 10],\n [14, 8, 22, -22, 20, 18, -10, -16, 12, -24],\n [-6, 1, -18, 20, 24, -14, 11, -4, -6, 6],\n [-7, -15, 11, 18, -14, -4, 17, -5, -15, -12],\n [-2, 2, -16, -10, 11, 17, -6, 13, -2, 26],\n [-12, 25, -8, -16, -4, -5, 13, 11, -1, 21],\n [0, -6, -14, 12, -6, -15, -2, -1, 14, -11],\n [16, -12, 10, -24, 6, -12, 26, 21, -11, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
903
|
math
|
train
|
math_arithmetic_matrix_determinant_level_6_6_382
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6
|
{
"role": [
"user"
],
"content": [
"Compute |A| for the matrix A =\n[[22, -4, -24, 28, -16, -9, 7, -10, 4, -18],\n [-4, 24, 5, -2, -8, -9, -2, 14, -3, -5],\n [-24, 5, 11, -8, -4, -5, 13, 2, 20, -8],\n [28, -2, -8, -10, -8, 4, 2, 11, -6, -7],\n [-16, -8, -4, -8, -10, -6, 22, 7, 0, -22],\n [-9, -9, -5, 4, -6, 22, 10, -14, -1, 15],\n [7, -2, 13, 2, 22, 10, 14, 12, 22, -12],\n [-10, 14, 2, 11, 7, -14, 12, -21, 15, 12],\n [4, -3, 20, -6, 0, -1, 22, 15, 11, 22],\n [-18, -5, -8, -7, -22, 15, -12, 12, 22, -24]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
70
|
math
|
train
|
math_arithmetic_matrix_determinant_level_6_6_383
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6
|
{
"role": [
"user"
],
"content": [
"What is the determinant of the matrix:\n[[-12, 22, 5, -18, -3, 22, 8, -9, -28, -15],\n [0, 7, -5, 17, 1, 18, -19, 19, 23, -18],\n [0, 0, 3, 20, -8, 3, 30, 6, -11, -14],\n [0, 0, 0, -27, 13, 19, -26, -19, -5, -3],\n [0, 0, 0, 0, 23, -26, -11, -11, -17, -26],\n [0, 0, 0, 0, 0, -5, 6, 28, 17, 18],\n [0, 0, 0, 0, 0, 0, -30, 17, 30, 10],\n [0, 0, 0, 0, 0, 0, 0, 26, 29, -4],\n [0, 0, 0, 0, 0, 0, 0, 0, -25, 21],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0
|
math
|
train
|
math_arithmetic_matrix_determinant_level_6_6_384
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6
|
{
"role": [
"user"
],
"content": [
"Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, -13, 7, -17, -30, 23, 18, 28, 23, 25],\n [0, -11, 25, 25, -10, -28, -21, 15, -12, -14],\n [0, 0, 11, -23, 11, -14, 18, 18, 28, 0],\n [0, 0, 0, 4, -29, -29, 2, 13, 15, 17],\n [0, 0, 0, 0, 20, 14, -29, -11, 1, -7],\n [0, 0, 0, 0, 0, 16, -29, -24, -15, 19],\n [0, 0, 0, 0, 0, 0, -5, 12, 10, 30],\n [0, 0, 0, 0, 0, 0, 0, -15, 25, 24],\n [0, 0, 0, 0, 0, 0, 0, 0, -15, -17],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0
|
math
|
train
|
math_arithmetic_matrix_determinant_level_6_6_385
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6
|
{
"role": [
"user"
],
"content": [
"Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-16, 16, 10, 3, 14, 0, -16, 14, -14, -4],\n [16, -1, 2, -6, 12, -22, 16, 4, -7, 12],\n [10, 2, -18, -22, -8, 4, 11, 12, 24, -24],\n [3, -6, -22, 23, -18, -2, 5, -16, -13, 16],\n [14, 12, -8, -18, -25, -24, 3, 18, 9, 12],\n [0, -22, 4, -2, -24, 12, -10, 10, 2, -5],\n [-16, 16, 11, 5, 3, -10, 22, 0, 14, -4],\n [14, 4, 12, -16, 18, 10, 0, 12, 4, 20],\n [-14, -7, 24, -13, 9, 2, 14, 4, 13, 4],\n [-4, 12, -24, 16, 12, -5, -4, 20, 4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
424
|
math
|
train
|
math_arithmetic_matrix_determinant_level_6_6_386
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6
|
{
"role": [
"user"
],
"content": [
"Determine the value of det(A) where A =\n[[-23, 25, 1, 9, 8, -29, -19, -25, 24, 13],\n [0, 9, -24, -4, -27, -7, 16, 29, -26, 22],\n [0, 0, 2, 21, 17, -13, 21, 14, -15, 24],\n [0, 0, 0, -13, 6, 22, 14, 1, 7, -28],\n [0, 0, 0, 0, -9, -24, 20, 10, 11, 9],\n [0, 0, 0, 0, 0, 12, -20, 4, 27, -10],\n [0, 0, 0, 0, 0, 0, 20, -6, 11, 23],\n [0, 0, 0, 0, 0, 0, 0, -10, 3, -13],\n [0, 0, 0, 0, 0, 0, 0, 0, -15, 11],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 25]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0
|
math
|
train
|
math_arithmetic_matrix_determinant_level_6_6_387
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6
|
{
"role": [
"user"
],
"content": [
"Compute |A| for the matrix A =\n[[-10, -27, -9, 5, -15, 10, 17, 24, 9, 24],\n [0, 7, 0, -9, -3, -11, 26, -29, -15, -25],\n [0, 0, -16, -9, 2, 1, 2, -2, 7, 2],\n [0, 0, 0, 27, -30, -26, 17, -14, -1, -4],\n [0, 0, 0, 0, -11, -22, 0, 26, 12, 9],\n [0, 0, 0, 0, 0, 23, -5, -6, -29, -5],\n [0, 0, 0, 0, 0, 0, 20, 18, 26, -17],\n [0, 0, 0, 0, 0, 0, 0, 5, 11, 12],\n [0, 0, 0, 0, 0, 0, 0, 0, -11, -21],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0
|
math
|
train
|
math_arithmetic_matrix_determinant_level_6_6_388
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6
|
{
"role": [
"user"
],
"content": [
"Determine the value of det(A) where A =\n[[-2, -28, 19, 22, 14, 23, -2, 4, 19, -30],\n [0, 14, -2, 15, -30, 30, -19, -29, 10, 6],\n [0, 0, 5, 27, 18, -3, -18, 6, 18, 28],\n [0, 0, 0, -10, 22, -8, 11, -30, 3, 30],\n [0, 0, 0, 0, -27, 11, -8, -29, 5, -14],\n [0, 0, 0, 0, 0, 22, 6, 15, -8, -27],\n [0, 0, 0, 0, 0, 0, 29, -3, -20, -1],\n [0, 0, 0, 0, 0, 0, 0, -1, 19, 25],\n [0, 0, 0, 0, 0, 0, 0, 0, -11, 17],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 11]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
600
|
math
|
train
|
math_arithmetic_matrix_determinant_level_6_6_389
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6
|
{
"role": [
"user"
],
"content": [
"What is the determinant of the matrix:\n[[-5, 2, 0, -4, -12, 8, -12, 2, 5, -1],\n [2, -29, -11, 4, -16, 0, 0, 9, 6, 18],\n [0, -11, 4, -10, 1, 2, -2, 4, 6, 11],\n [-4, 4, -10, -21, -4, -21, 10, 14, 8, 20],\n [-12, -16, 1, -4, -14, 0, 0, -24, 12, -11],\n [8, 0, 2, -21, 0, -25, -12, -9, -4, 7],\n [-12, 0, -2, 10, 0, -12, 9, -9, -7, -8],\n [2, 9, 4, 14, -24, -9, -9, 17, 28, -8],\n [5, 6, 6, 8, 12, -4, -7, 28, -14, -20],\n [-1, 18, 11, 20, -11, 7, -8, -8, -20, -21]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
464
|
math
|
train
|
math_arithmetic_matrix_determinant_level_6_6_390
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6
|
{
"role": [
"user"
],
"content": [
"Determine the value of det(A) where A =\n[[-29, 8, -6, 6, 3, 8, 3, 7, -6, 10],\n [8, -20, 4, -12, -2, -1, -13, -2, 13, 18],\n [-6, 4, -27, -16, 4, -2, -20, 8, -5, -9],\n [6, -12, -16, -2, 14, 2, 12, 17, -14, -4],\n [3, -2, 4, 14, 24, 4, -12, 14, -6, -22],\n [8, -1, -2, 2, 4, 12, 3, 12, 10, 12],\n [3, -13, -20, 12, -12, 3, -20, -1, -8, -2],\n [7, -2, 8, 17, 14, 12, -1, -13, -2, -6],\n [-6, 13, -5, -14, -6, 10, -8, -2, 22, 2],\n [10, 18, -9, -4, -22, 12, -2, -6, 2, -26]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
731
|
math
|
train
|
math_arithmetic_matrix_determinant_level_6_6_391
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6
|
{
"role": [
"user"
],
"content": [
"Compute |A| for the matrix A =\n[[-28, 26, 2, 6, -5, -12, 7, 16, 0, 2],\n [26, 10, 0, -8, 24, -4, 8, -12, -3, 10],\n [2, 0, -9, -4, -2, -4, 6, 4, -20, -2],\n [6, -8, -4, 11, -7, 2, 7, -19, 2, -7],\n [-5, 24, -2, -7, 25, -1, -2, -2, 0, -14],\n [-12, -4, -4, 2, -1, 1, 0, 2, -15, -2],\n [7, 8, 6, 7, -2, 0, 15, -14, 2, 19],\n [16, -12, 4, -19, -2, 2, -14, -19, 8, -26],\n [0, -3, -20, 2, 0, -15, 2, 8, 6, -2],\n [2, 10, -2, -7, -14, -2, 19, -26, -2, -9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
255
|
math
|
train
|
math_arithmetic_matrix_determinant_level_6_6_392
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6
|
{
"role": [
"user"
],
"content": [
"Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-25, -23, -20, -16, 28, 29, 16, 7, 16, -10],\n [-12, 6, 10, -30, -19, 22, 27, -13, -14, 12],\n [-8, -15, -20, 23, 25, -12, -8, 27, 30, 19],\n [7, -9, -26, 2, 15, 29, -23, -14, 22, -5],\n [23, 30, -3, 17, -1, 6, 27, 25, -24, -30],\n [4, 21, -3, 19, -20, -5, 11, -24, -11, 8],\n [12, -21, -17, 1, -19, -6, -6, 16, -13, 18],\n [-15, -18, 15, 21, -6, -2, 30, -17, 16, 9],\n [-22, -30, 23, 18, 23, 20, -14, -18, 22, -6],\n [-22, -25, 15, 10, -12, 20, -7, 5, -21, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
47
|
math
|
train
|
math_arithmetic_matrix_determinant_level_6_6_393
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6
|
{
"role": [
"user"
],
"content": [
"What is the determinant of the matrix:\n[[11, 14, 22, 24, -12, 12, -15, 9, -2, -16],\n [14, 7, 12, 6, 4, -25, 18, 3, 12, -4],\n [22, 12, 0, 12, 2, 8, -8, -3, -6, 0],\n [24, 6, 12, 0, 17, 0, 14, 6, 12, -19],\n [-12, 4, 2, 17, -22, 2, 4, -10, -3, 10],\n [12, -25, 8, 0, 2, 12, -12, 16, 1, 0],\n [-15, 18, -8, 14, 4, -12, -8, 20, -8, 7],\n [9, 3, -3, 6, -10, 16, 20, 29, 13, -8],\n [-2, 12, -6, 12, -3, 1, -8, 13, -23, 0],\n [-16, -4, 0, -19, 10, 0, 7, -8, 0, -5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
35
|
math
|
train
|
math_arithmetic_matrix_determinant_level_6_6_394
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6
|
{
"role": [
"user"
],
"content": [
"What is the determinant of the matrix:\n[[-28, 13, -30, -22, 19, -24, -18, 21, 13, -10],\n [-12, 2, -26, -19, 29, 6, -30, -18, -6, 7],\n [-21, 11, 11, 4, -20, -28, -8, -29, -7, -5],\n [28, 29, 23, -2, -1, 30, -19, -26, 0, -24],\n [22, -28, 3, 29, -1, 5, 21, -11, 6, -2],\n [-12, -2, -3, 24, 25, 22, -28, 14, -24, -7],\n [-16, 27, -15, 5, 29, 9, -9, 8, 12, 9],\n [18, 3, -20, -27, 29, -23, -18, 11, 26, -22],\n [-20, 18, -1, 1, -27, 6, -28, -21, -3, -26],\n [-5, 12, -18, -14, -28, -12, 10, 9, 3, -10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
199
|
math
|
train
|
math_arithmetic_matrix_determinant_level_6_6_395
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6
|
{
"role": [
"user"
],
"content": [
"Determine the value of det(A) where A =\n[[25, 13, -20, -30, 7, 9, 15, -16, -6, -4],\n [0, -7, 28, 30, -22, 26, 16, -12, 24, 9],\n [0, 0, 4, 19, -14, 20, -4, 21, -10, -9],\n [0, 0, 0, -13, -20, 8, 7, 26, 19, 7],\n [0, 0, 0, 0, -6, -5, 14, 8, 30, -11],\n [0, 0, 0, 0, 0, -7, 29, -4, 12, -28],\n [0, 0, 0, 0, 0, 0, 17, 4, 1, 20],\n [0, 0, 0, 0, 0, 0, 0, -29, -15, -19],\n [0, 0, 0, 0, 0, 0, 0, 0, 16, 14],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
800
|
math
|
train
|
math_arithmetic_matrix_determinant_level_6_6_396
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6
|
{
"role": [
"user"
],
"content": [
"What is the determinant of the matrix:\n[[26, -14, -30, 15, -7, 2, -21, -28, -26, -28],\n [0, 30, -13, -18, -7, 20, 12, -25, -11, 17],\n [0, 0, -3, 25, 8, 11, 29, 2, -19, -20],\n [0, 0, 0, 16, 24, 18, 20, 24, -7, 0],\n [0, 0, 0, 0, -10, 1, 5, 6, 8, 23],\n [0, 0, 0, 0, 0, -18, -11, -24, 14, -22],\n [0, 0, 0, 0, 0, 0, 16, -4, 17, -7],\n [0, 0, 0, 0, 0, 0, 0, -21, -2, 7],\n [0, 0, 0, 0, 0, 0, 0, 0, -20, 24],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 18]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0
|
math
|
train
|
math_arithmetic_matrix_determinant_level_6_6_397
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6
|
{
"role": [
"user"
],
"content": [
"Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-26, -13, 2, 8, 8, -4, -4, -13, 7, 15],\n [-13, -18, -15, 0, -10, 4, 26, 19, 14, -14],\n [2, -15, -12, -1, -20, -8, 10, 6, -23, 12],\n [8, 0, -1, 26, -20, -12, -7, 4, 7, 4],\n [8, -10, -20, -20, 15, 14, -18, -14, -20, 2],\n [-4, 4, -8, -12, 14, 17, -12, -10, -8, 0],\n [-4, 26, 10, -7, -18, -12, 29, -22, 12, -6],\n [-13, 19, 6, 4, -14, -10, -22, -21, 8, -2],\n [7, 14, -23, 7, -20, -8, 12, 8, 6, 2],\n [15, -14, 12, 4, 2, 0, -6, -2, 2, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
76
|
math
|
train
|
math_arithmetic_matrix_determinant_level_6_6_398
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6
|
{
"role": [
"user"
],
"content": [
"Compute |A| for the matrix A =\n[[0, -10, 1, -10, -13, 6, 24, 10, 6, -2],\n [-10, 20, -23, 10, 8, 1, -13, 6, -10, 0],\n [1, -23, 13, 20, 13, 0, 1, 4, 14, 9],\n [-10, 10, 20, -25, -15, -7, -18, 22, 1, -4],\n [-13, 8, 13, -15, -15, 8, 4, -4, -2, 0],\n [6, 1, 0, -7, 8, 29, -16, 9, 18, -5],\n [24, -13, 1, -18, 4, -16, -22, -14, -12, 20],\n [10, 6, 4, 22, -4, 9, -14, -18, -10, -24],\n [6, -10, 14, 1, -2, 18, -12, -10, 1, 26],\n [-2, 0, 9, -4, 0, -5, 20, -24, 26, 11]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
316
|
math
|
train
|
math_arithmetic_matrix_determinant_level_6_6_399
|
arithmetic_matrix_determinant6
|
expert (level 6,7)
| 6
|
{
"role": [
"user"
],
"content": [
"What is the determinant of the matrix:\n[[20, -5, 0, 14, 5, 26, 7, 23, -18, -28],\n [0, -1, 1, 26, -13, -3, -2, -1, 28, -5],\n [-24, -19, 17, 11, -29, -2, -17, -6, 27, -18],\n [-5, -17, -23, 15, -19, 21, -7, -8, 7, -18],\n [-30, -7, 24, 18, 13, -27, -20, 23, -26, 16],\n [30, -21, -16, -30, 14, 4, 8, 8, 16, -25],\n [22, -28, 2, 20, 19, -3, -19, 13, -10, 0],\n [-10, -2, 7, -21, -1, -8, 30, 15, -9, 22],\n [28, 6, -12, -3, -23, -1, -5, -1, -9, 8],\n [-7, 27, 21, 18, 29, -7, 10, 13, -9, -27]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
459
|
math
|
train
|
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