id
stringlengths 31
70
| setting_key
stringclasses 167
values | difficulty
stringclasses 4
values | level
int64 1
7
| messages
listlengths 1
1
| ground_truth
stringlengths 1
19
| dataset
stringclasses 1
value | omega_split
stringclasses 1
value |
|---|---|---|---|---|---|---|---|
math_arithmetic_matrix_svd_level_7_7_968
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[6, 3, -7, -21, -26, -18, 5, 6, -9, 10, -8, 6],\n [-22, -15, -26, -21, -10, -19, -22, 8, 1, -12, 1, -3],\n [-1, -19, 8, -11, -20, -10, 24, 8, 4, -20, 24, -24],\n [-9, 26, 0, -10, 5, -16, -15, 19, 9, -15, -15, -7],\n [15, -24, 4, -22, -7, 13, 16, 20, 15, -26, -16, 18],\n [14, 9, 4, -3, -12, -25, 2, 14, -5, 14, -16, 4],\n [-7, 16, 12, -12, 8, -10, -23, 25, 4, 2, 3, -22],\n [2, -7, -18, 26, 10, -13, 17, -9, 22, -10, -10, -21],\n [-6, 19, 15, -17, 17, 1, 10, 18, -6, -26, 14, -23],\n [10, 18, 25, 21, -21, -2, -26, 9, 15, 8, -24, 17],\n [13, -3, -4, -1, -22, 7, 26, 25, -13, -3, 11, 6],\n [26, -10, 6, 17, 17, -12, 8, -13, -26, 19, -13, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
90
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_969
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[18, 10, -15, 26, 8, 5, -25, 6, -9, 20, -11, -2],\n [-1, -22, -11, 17, -11, -16, -19, -24, 26, -11, -20, 1],\n [-25, 24, 8, 4, -16, 14, -16, -26, 3, 3, 6, -15],\n [-17, 17, 19, 16, -23, 15, 22, 6, 11, 4, 4, -22],\n [-6, -9, -9, -23, 23, -7, 26, -7, 21, 1, 20, -14],\n [8, -9, 6, 10, 9, -18, -1, -26, -2, -3, 3, 15],\n [-15, 17, -12, -7, 0, 2, -25, -12, 8, -17, -1, 7],\n [-19, -26, -12, -23, -24, 18, 15, -25, -8, -8, 19, 14],\n [-8, -7, 22, 10, -25, -2, 12, -5, 7, -5, -15, 19],\n [12, 19, -15, 21, 19, 26, 4, 26, 5, 9, -13, -1],\n [1, -26, -17, -4, 8, -12, 26, 18, -19, -25, -7, 14],\n [16, 2, -25, 13, 14, 17, 24, -12, 26, -23, 15, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
90
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_970
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[1, 13, 16, 10, -6, -12, 6, 26, 22, -15, 3, -23],\n [12, -16, 17, 0, 21, -9, -13, -12, 22, 7, -4, 8],\n [-22, -26, -1, -17, -12, 5, 15, -3, 9, 18, -11, -17],\n [7, 13, -13, -22, -9, -19, 4, 17, -9, -14, 10, -16],\n [-24, -11, -19, -10, 11, -14, 22, 8, 18, 13, -19, -8],\n [15, -12, -20, 23, -26, -14, 22, -8, -25, -5, -19, 16],\n [-2, -1, -15, -24, -6, -22, -15, 0, -26, 16, -24, 25],\n [26, -17, -14, -8, 4, -14, 25, 3, -13, 5, 15, 22],\n [11, 10, -13, 19, 10, 1, -7, -2, -16, 0, 2, -22],\n [-4, 24, 20, 22, -10, -24, 24, -22, -19, 6, -13, 15],\n [4, -19, -26, -22, 24, 12, -22, 7, 20, -26, -17, 11],\n [11, -13, -19, -2, 2, 23, 10, -6, 4, 19, 15, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
89
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_971
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[14, -6, 26, -24, 5, -21, -20, 24, -12, 7, 19, 19],\n [-15, -9, -2, 11, -25, -6, -4, 6, 0, 16, 2, 20],\n [11, -10, -19, -6, -4, 25, -9, 17, -19, 25, -3, -18],\n [2, -16, 18, 9, -19, -23, 19, -3, 22, -25, -15, -15],\n [-1, -8, 23, -1, -3, 15, -2, 14, -11, -26, 5, 21],\n [-3, 13, 24, 7, 23, -7, -4, 1, 25, -9, 5, 26],\n [19, 12, 12, 1, 10, 25, -1, 0, 17, 0, 18, -10],\n [-12, 21, -14, -5, 16, 8, -4, -26, 11, -19, 26, -22],\n [12, 8, 14, -13, -25, -24, -8, -17, -25, 18, -13, -8],\n [18, -20, -24, -26, 25, -4, -14, 11, 17, -17, 8, 4],\n [6, -3, -14, 7, 26, -8, -7, -24, -8, 20, 4, -8],\n [15, 0, -16, 20, 13, -16, -10, 7, 23, -18, 12, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
84
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_972
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-4, -19, -14, 7, 15, -10, 21, 17, 11, -12, 4, 20],\n [21, -24, 18, 23, 8, 9, -22, -1, -1, 25, -3, -21],\n [-20, 25, 1, 18, -13, 12, -6, -16, -15, 23, 23, 7],\n [8, 25, -20, 26, -4, -26, -7, 5, 7, 23, -7, -13],\n [-22, -3, -6, -15, -25, -17, -14, 4, 19, -3, -1, 6],\n [14, -3, -26, -18, 4, -3, 16, -1, 12, 26, -5, 6],\n [5, 6, -18, -12, -5, -11, 8, -2, 8, -2, 19, 10],\n [22, 26, -17, -11, -9, 18, 23, 2, -10, -23, -23, 26],\n [-12, -23, -14, 23, 26, -21, -22, 6, -21, 7, -22, 21],\n [9, -14, 1, -20, -18, -1, 6, -4, 10, -1, 25, -16],\n [22, -14, 25, 0, -25, -11, 24, 2, -7, 5, -4, -18],\n [5, -23, 23, 15, 20, 18, 21, -17, -23, 21, -16, -25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
570
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_973
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[1, -15, 13, -6, 18, 7, 7, 9, 23, -24, 12, -21],\n [-26, 14, -15, 12, -26, -7, 9, 11, 21, 20, -24, 23],\n [24, 18, -7, 19, 19, -19, -16, 17, -26, 3, 14, 25],\n [-13, -7, 19, 3, 18, -15, -15, 25, 12, -25, -4, -16],\n [21, -14, -9, -8, 0, -16, 26, 3, -26, -14, -19, -5],\n [-7, -13, -13, -11, -8, 12, 2, 11, -18, 23, -21, -1],\n [22, 9, -7, 14, -2, -19, 20, 13, 0, -6, -16, -8],\n [-14, 20, -22, -1, -20, -14, 21, -3, 21, -3, 7, 12],\n [-23, -7, -14, 26, 3, 10, -4, 17, -14, 14, 21, 11],\n [18, -13, 9, 14, -22, -16, -11, -15, -10, 4, -19, -15],\n [-19, -14, -4, -22, -19, -24, 16, -22, 21, 15, 15, -2],\n [5, -11, -16, -3, 14, -3, 12, 19, 19, -5, -9, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
87
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_974
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-26, -15, -4, -19, 6, -15, -10, 3, 12, 16, -14, -6],\n [-18, 1, -20, -9, 23, 15, 6, 19, -4, 26, -26, 12],\n [-8, -8, -23, -20, 2, 21, 12, -16, 2, -19, 18, -18],\n [-22, 4, -17, 16, -3, -10, 20, -16, 7, -3, -19, 17],\n [12, -3, -25, -19, 4, 20, 17, 8, -23, -15, 12, -11],\n [-5, -10, -2, 24, -12, -7, 4, 23, -22, 3, 0, 19],\n [-13, 19, -10, 3, 19, -23, 15, -23, -24, -20, 25, 12],\n [8, -14, 9, 24, 9, 20, 1, 25, 5, 17, -13, 9],\n [8, 11, 20, -22, -21, -15, 12, 25, 16, 22, -15, -19],\n [18, -9, 24, -9, -17, -21, -22, 18, -4, -2, -20, 16],\n [18, -22, 4, -8, 24, 9, 17, 23, 8, 16, -18, -3],\n [-9, 17, -18, 26, 11, 7, 6, -23, -7, -4, 23, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
532
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_975
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-1, 16, -26, 12, 16, 5, 21, 24, 1, -3, -14, 6],\n [-15, 6, -13, -14, 21, 10, 0, -23, -23, 13, 20, -11],\n [12, 13, -9, -11, 20, 4, -1, -4, 25, 21, 21, -25],\n [11, -16, -22, 20, -13, -11, 21, 14, 24, 10, -6, -19],\n [-13, -18, -15, -12, -2, -6, 19, 7, -1, -23, -2, 13],\n [5, 2, -5, 7, -8, 23, -21, -7, -11, 6, -18, -5],\n [7, 20, -8, 14, 14, 10, -23, -22, -15, 6, 24, -18],\n [17, 2, 3, 2, 18, 25, -10, 8, -14, 19, 9, -23],\n [-26, 11, 16, 0, 1, -2, -3, -25, -4, 24, -5, -9],\n [25, -11, 5, -24, -26, 7, 18, -1, 19, 13, 19, -21],\n [17, 9, -18, -20, 4, 6, -23, -21, -16, 13, -14, -18],\n [24, -9, -1, -4, -4, 24, -22, -17, 20, 13, -8, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
102
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_976
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-12, -8, -23, 8, 10, -15, 4, -11, 13, -6, -7, 23],\n [-5, 17, -22, -19, -19, 6, 0, 3, 1, 13, 24, -9],\n [25, -17, 13, -14, 10, 16, 13, 24, -4, -8, -4, 14],\n [-11, -15, 9, -23, -15, 0, -13, -11, 26, 2, -15, 26],\n [-12, -26, 1, -19, 5, -2, 8, -15, -21, 4, -18, 25],\n [-2, -7, 11, -12, 9, -1, 10, 22, 14, -16, 0, 12],\n [-6, 26, -21, -16, 19, 4, -16, 24, 18, -19, -8, 5],\n [-1, 19, 10, 16, 26, 7, 20, -11, 6, 8, -17, 9],\n [-4, 21, 14, -23, -8, -8, 15, 15, -13, 6, 21, 25],\n [10, 19, -9, -19, -17, 4, 8, -2, -2, 13, 20, 19],\n [-24, -12, 5, -6, 6, 12, 0, -13, 9, 19, 14, -17],\n [-3, -17, 4, 12, 20, 1, -23, 23, 21, -8, 13, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
515
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_977
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[5, -21, 24, -17, 18, -11, -25, -19, 14, 12, -22, 3],\n [-19, 2, -24, -14, 25, 0, 24, -15, 24, 13, 24, -21],\n [12, 22, -12, 19, 20, -19, 13, 25, -3, 5, 4, 11],\n [-24, 21, 8, -14, 20, 15, 14, -12, -1, -15, -2, 1],\n [-8, -18, 8, 18, 9, 5, -24, -22, 25, 14, -9, 15],\n [24, -12, -2, -9, -20, -5, -3, 8, -5, 0, -25, -16],\n [20, -1, -20, -8, 10, -8, -17, 20, 4, -26, -10, -17],\n [9, -6, -10, 15, 17, 16, -24, 24, 23, -5, 3, 23],\n [9, -22, -24, -26, -10, 22, 25, -5, 0, 6, -6, -26],\n [-23, 14, -21, 1, -15, 18, 25, -4, 16, -15, 15, 21],\n [22, 18, 6, -6, 14, 13, 0, 23, 5, -26, 5, -24],\n [6, -26, -3, -8, -9, 5, 17, -21, -10, -15, 7, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
94
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_978
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[12, -25, -7, -7, 20, 12, 24, 5, -24, -1, 14, -15],\n [23, -24, 1, -18, -1, -21, -22, -18, 19, 7, 1, -1],\n [8, -26, -23, -14, 13, 26, -6, -9, -7, -23, 5, 0],\n [-2, -20, 18, 3, -4, 2, -6, 6, -9, 0, -13, 13],\n [4, 15, -19, -24, 8, 11, -16, 9, 25, 21, 16, 25],\n [7, -4, -22, 3, 10, -11, -13, -20, 26, 6, -25, 19],\n [-22, 18, 18, 12, -12, 15, -25, -3, 2, 2, -6, -2],\n [-5, -8, -14, 11, 6, 6, -15, 19, -4, 2, 2, 16],\n [-26, -3, -22, 8, 18, -22, -14, 5, 15, 0, -3, -24],\n [-26, 2, 18, -5, -22, 16, -6, -15, 1, -16, -12, 11],\n [8, 21, 18, -11, 10, -12, 5, -11, 6, 13, -7, 10],\n [12, 5, -17, -11, -22, -7, 0, 16, 23, -7, -14, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
85
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_979
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[17, 23, -12, 11, 0, 15, -10, -17, 9, 13, -22, 24],\n [23, 21, 0, 1, -23, -20, -19, -12, 14, 2, 12, -18],\n [-7, -26, -20, 7, 20, -17, 14, 21, -21, -2, -15, 13],\n [14, 12, -13, -16, -15, -8, 15, 1, 26, -8, 2, 18],\n [8, -4, -11, 10, -6, 13, -26, 19, 25, 10, -2, -11],\n [6, -2, -5, -24, -24, -16, 16, 25, -22, 17, -2, 11],\n [26, -11, 5, 2, -21, -5, -18, -17, -13, 20, 12, -7],\n [-22, -20, 13, -13, -12, -10, -7, -11, 14, -6, -16, -23],\n [-2, -25, -25, 0, 4, 20, -19, 21, -19, -22, -5, 16],\n [-22, 13, 21, -21, 11, -20, -9, -2, -24, -2, -6, 4],\n [19, 22, 15, -11, 25, -5, 24, 2, -15, 19, 16, -26],\n [-1, -17, -2, -2, 16, -23, -9, 16, -19, -20, -10, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
571
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_980
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[15, 17, -6, -25, -14, 5, -14, 2, -22, -1, 11, 5],\n [21, -9, -10, -7, -12, -12, 20, -23, -18, 17, 19, 6],\n [-17, 20, 16, -26, 13, 26, -18, -5, -1, 8, 6, -17],\n [11, -8, -23, -8, -20, -15, 0, 5, 0, -6, -22, -8],\n [24, 25, 26, -20, -13, -18, 10, 23, -18, -22, 21, -18],\n [25, 16, 3, -13, -24, 25, -3, 1, 12, -16, -10, -9],\n [24, -10, -2, 14, -13, -6, -16, 20, 0, -23, 24, 14],\n [7, 13, -20, -9, -8, -9, -12, -16, -15, 8, 9, 26],\n [23, -15, -11, 1, 17, 12, 17, 9, 3, -11, -11, 22],\n [-7, -18, 19, -22, 4, -9, 17, -5, 12, -25, 23, -24],\n [20, 1, -16, -17, -7, 4, 26, 24, 18, 21, 25, -5],\n [-9, -15, -12, 7, 18, 1, 17, -12, 8, -10, 11, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
565
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_981
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-1, 2, 25, -2, -23, 0, 15, -5, -3, 26, -8, 14],\n [0, -8, 20, 14, -14, 4, -25, 0, -19, -15, 2, 2],\n [-5, 3, -18, -22, 9, -14, 20, -25, 6, -23, -17, 6],\n [-25, -15, -11, 8, -18, -24, 1, 25, -11, 13, -8, -16],\n [11, 19, 4, -26, 17, 3, -6, -12, -11, -23, -3, 13],\n [-4, -10, 8, -1, 8, -12, -12, 0, -19, 26, -12, 26],\n [-19, 24, -23, -26, -2, 8, -19, 22, -10, 1, -21, 16],\n [-21, -26, -24, 25, -18, -12, 13, -7, -11, -17, -13, -11],\n [-12, 14, -1, -17, 13, -15, 10, -13, -2, 3, 26, 3],\n [8, -12, 4, 11, 24, -9, -20, -24, -22, -2, -11, -12],\n [-7, 14, -5, 8, 0, -15, 6, -3, -1, 25, 11, 7],\n [-14, 1, -7, -19, 23, -11, 7, 5, 21, 3, 8, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
517
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_982
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[21, -18, 4, -8, 16, 7, -11, -3, -11, -12, 4, 25],\n [-20, 17, -12, -25, 12, 25, -5, -3, -2, -15, 25, 24],\n [-13, 7, 19, -7, -13, -9, 8, -10, 21, 18, -4, -5],\n [22, 4, 2, -2, 5, 4, -21, 10, -10, 20, 4, -6],\n [-25, -20, 0, -5, -23, 0, 24, 18, 5, -6, 8, -18],\n [1, -17, 23, -4, -3, 21, -23, -10, 21, -3, -26, 10],\n [-25, 13, 21, 26, -21, -13, 9, -6, -2, -19, 25, 0],\n [-13, -23, 19, -19, 0, -8, 3, 1, 0, 10, 17, -24],\n [22, 1, -8, 11, 0, -4, -8, -14, 3, 14, 23, 19],\n [-19, 2, 16, 23, 23, 20, -21, -10, 2, 13, 25, 21],\n [-25, 6, 18, 12, 24, 8, 4, -15, 4, -1, 17, 5],\n [22, 22, 23, -24, -7, 26, 20, -25, 12, 18, -14, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
551
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_983
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[24, -21, 15, -19, -1, -17, 11, 17, -26, -25, 16, 8],\n [-26, -23, -24, -3, -10, 0, -2, -7, 12, 17, 24, 3],\n [-21, -20, 0, -22, -1, 9, -16, 15, -4, -24, 23, -12],\n [17, 26, -2, -11, 5, -1, -22, -17, -16, 6, 1, -11],\n [17, -25, 2, 17, -25, -5, -16, 8, 5, 10, 20, -22],\n [0, 24, -15, -19, -24, 5, -5, 1, -1, 18, -6, -16],\n [0, 16, -20, 11, 16, -18, 20, 21, 7, 16, -1, -21],\n [-15, 10, 23, 17, 13, -26, 8, -23, 13, 23, -19, -25],\n [-15, 24, -19, 14, 4, -6, 4, 5, -7, 20, -8, 20],\n [3, 24, -18, -7, -9, 21, -14, 3, 20, 2, 25, 24],\n [3, 20, -22, -23, 23, 19, 4, 15, 6, 22, -26, -8],\n [-12, -25, -23, -24, -4, 13, 16, 26, -21, 3, -4, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
99
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_984
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[22, -12, 18, 20, 23, -10, -18, -25, 23, 26, 14, 2],\n [24, 15, 19, 4, 5, -26, 3, 1, -1, -9, -26, 14],\n [25, 21, -8, 8, 6, -19, 25, 22, 0, 10, 15, -19],\n [17, 21, 5, -8, 3, 9, -17, 9, -11, -24, -5, 24],\n [-5, -6, 3, 0, -25, -19, 16, -4, 12, 11, 14, 9],\n [-13, 26, 4, 20, 24, -8, 3, -11, -15, -3, 15, 11],\n [5, 23, -8, 13, 20, -22, 18, 19, 20, -25, 24, 5],\n [0, -25, 10, 10, -5, 7, 0, -10, 12, -4, -17, -5],\n [-12, 23, 13, 9, 16, 12, -11, 1, 8, 5, 25, 20],\n [-3, -6, 14, -8, 5, 19, 7, 25, -9, -16, -16, -9],\n [-26, 13, -26, -3, 14, -5, -20, -10, 22, -15, -26, -24],\n [20, 3, -4, -19, 17, -10, -21, -15, -6, -16, -25, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
546
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_985
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[21, -7, 4, 9, -3, -5, -18, 22, -10, 7, 26, -16],\n [-21, 24, 22, -4, 21, 22, 20, 18, 22, 13, -1, -18],\n [-19, 22, 25, 19, -1, 25, -15, 6, 18, -20, -11, -1],\n [-2, 8, 16, 2, 23, 15, 1, -11, -8, 13, -21, 0],\n [-24, 7, -10, 5, -3, 8, 8, 5, 26, -12, 10, -2],\n [-6, -13, -4, -20, -22, -13, -8, 16, -20, -19, -23, -21],\n [10, -17, 23, 22, -13, -14, 11, 21, 15, -20, -6, 6],\n [-16, -21, 9, -16, 7, 3, -18, -20, 19, 10, -9, 22],\n [2, -6, -13, -11, -1, 26, 4, 24, -16, 5, -1, 6],\n [10, -16, -7, -14, 7, 6, 16, -23, -19, 23, -16, -25],\n [-5, -23, 15, -2, 25, 17, 23, -12, -15, 6, 5, -21],\n [16, -26, 11, 13, 11, -7, 17, 23, -22, 10, 13, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
559
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_986
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-25, -13, -10, 23, -9, -10, 13, 4, 15, 4, 9, -8],\n [5, -10, -3, 18, 13, -23, -22, 25, 26, 20, 25, 14],\n [-26, -1, 15, -24, -4, -14, -5, 4, -19, 3, 19, -15],\n [-5, 16, -12, 3, -3, 22, -2, 26, -25, -26, -7, 18],\n [17, -1, -19, -8, 4, -12, 15, 25, -25, -25, 23, 2],\n [6, -17, 21, 19, -6, -6, 16, -14, 24, -11, -8, -3],\n [-4, -23, 4, -19, 15, -2, -4, -16, 1, 18, -4, 18],\n [26, 18, 16, 21, 20, 9, 7, 21, -16, 22, -19, 7],\n [-19, 25, -10, -5, -19, -26, -13, -22, 0, 21, 22, -4],\n [-15, 25, 3, -19, 13, -25, -22, -14, -10, 8, -12, -15],\n [8, 15, 21, 24, -24, -17, -25, -12, -20, -7, -19, 20],\n [-1, -19, 3, 18, -7, 4, 2, 26, 3, 4, -23, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
590
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_987
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[17, 3, -5, 5, -15, 3, -22, -25, -21, 16, 16, 8],\n [-17, -11, 21, -5, 24, -13, 13, -11, 21, 12, -26, -11],\n [-7, 5, -25, -5, -22, -25, 22, 12, 17, 14, 5, -16],\n [-1, 24, 4, -12, -15, -1, 20, 22, -16, 22, -5, 1],\n [-5, -6, 17, -17, 26, 11, -2, 12, -13, 21, 8, -18],\n [11, 10, -23, -12, 2, -17, 6, -20, 26, -10, -23, -17],\n [-26, 15, -7, -20, -18, 5, 1, 1, -25, -23, -10, -21],\n [-19, 19, -15, -8, 2, 5, 1, -22, 16, 22, -15, -22],\n [6, 26, 4, -2, -20, 12, -2, 2, -16, -6, -4, -21],\n [11, -4, -17, 8, -22, -9, -6, -12, -15, 13, -20, 1],\n [8, -20, -9, 21, -7, -1, 7, 12, 10, -13, -12, -11],\n [-4, 7, -7, -8, -17, 23, 7, 13, 11, 24, -19, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
543
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_988
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-6, -26, 18, 22, 15, -9, 22, -4, -11, 20, 15, -2],\n [-22, -16, 16, 19, -21, 20, -13, 17, -1, 0, -13, 16],\n [2, -9, -9, -13, -20, 1, -22, 22, 13, 22, -12, 22],\n [7, -22, 25, -23, -10, -26, -17, 7, 23, 6, 15, 0],\n [-3, 24, 26, 16, 1, -8, -25, -26, 18, -2, -24, -20],\n [-2, -12, 25, -23, -25, -21, 8, 7, -6, -5, 25, 14],\n [2, 22, -13, 19, 15, 22, -20, -22, -12, 25, 21, -13],\n [10, 8, 22, 1, 10, -1, -21, 21, 20, -19, -17, 19],\n [-5, -17, -8, 5, -13, -3, -9, 0, -9, -23, 2, 4],\n [-24, -10, -24, -20, 4, 0, 11, -24, -14, -9, -5, 18],\n [-15, 12, 23, -8, 19, 3, 26, 17, 4, -10, 1, 14],\n [-23, -22, 8, -20, -11, -1, -7, -23, 5, -18, -24, 26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
574
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_989
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[24, 5, 18, 23, 26, -25, 1, -22, -13, 18, -17, 17],\n [5, 11, 20, 1, -26, -24, 12, -2, 3, 9, 11, 3],\n [-12, 4, 16, -2, -4, 19, -1, 23, -5, -11, -10, 0],\n [-10, -10, -7, -25, 9, -4, 1, -1, 16, 23, 18, 24],\n [-15, -10, 14, 1, -16, 11, 18, -16, -12, -1, 2, -1],\n [-4, -16, -23, 25, -17, 15, 13, 6, -23, 9, -19, -5],\n [-6, 3, 3, -11, 19, -25, -4, 7, 3, 1, -22, 8],\n [-18, 11, 19, -8, 14, -20, 26, -1, -13, 5, 12, 3],\n [-17, -25, 11, -22, -21, 1, -12, 2, 3, 17, 17, 4],\n [4, 8, -1, -18, 26, 21, 26, -20, -14, -7, 24, 1],\n [20, 3, 24, 14, 0, 22, 3, 14, -3, 3, -26, -3],\n [-7, -19, -10, 4, -23, 7, 6, 2, 25, -8, -13, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
86
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_990
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-26, -5, 19, -23, 25, 8, 23, 25, 12, 6, -11, 18],\n [8, -15, 9, 24, 19, -20, -23, -15, -20, 19, -12, -21],\n [-10, -10, 17, -23, -20, 9, -20, 11, 9, 15, 6, -4],\n [1, 1, 6, -5, 12, -5, -23, -3, -11, 23, 19, -14],\n [-12, 6, 3, -4, 15, 23, -22, 26, 12, 7, 14, -22],\n [23, 17, -23, -11, -16, 24, 0, -4, 6, -4, -14, -22],\n [5, 13, -17, -12, -12, -4, 18, 7, -23, -14, 2, -18],\n [-22, -15, 7, 25, -19, -7, -11, -3, -7, -19, 2, -8],\n [25, 15, -2, 10, -24, -8, 25, 7, -20, -18, -19, -8],\n [10, -19, 20, -3, -25, 2, -15, 22, 21, -22, -26, -14],\n [12, -19, -8, 19, 1, -17, 22, 23, 7, -17, -9, -17],\n [-6, -25, -18, 21, 11, -20, -24, -1, -20, 25, 13, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
101
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_991
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[10, 8, 19, 0, 11, 8, -20, 11, -7, -4, 23, 2],\n [26, -5, -6, 15, -22, 13, 26, 20, 21, 16, -17, 6],\n [-26, 22, 9, -11, -8, -22, -4, -24, 19, 23, -9, -24],\n [15, 24, -24, -13, -19, 5, 3, -8, -21, -18, 21, 3],\n [-21, 21, 4, 15, 26, -6, 13, -12, 16, -6, 16, -13],\n [11, -15, -12, 10, -16, 3, 8, 8, 15, 15, 25, 10],\n [1, 14, -17, -16, -25, -25, 19, -10, 13, 22, -14, 11],\n [-25, 25, -1, 0, 26, 23, 26, 12, 10, 6, -9, 2],\n [-23, 21, 3, 11, -10, 21, 13, -14, -7, 9, -22, 0],\n [-4, -16, 8, -9, 17, 26, -24, 4, 16, -12, 8, 12],\n [-21, 2, 0, 1, -24, -4, -1, 0, -21, 6, -13, 26],\n [25, -24, -8, 13, -8, 0, 23, 10, 24, 15, 21, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
552
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_992
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[13, 14, -25, 18, -13, 22, 1, -17, 11, 1, -14, 1],\n [18, -10, -22, 20, -22, -8, 7, 14, 16, 12, 4, -2],\n [24, -26, 23, -5, 11, 21, 2, -25, 14, 15, 3, -10],\n [9, 25, -13, -10, 1, 26, -21, -18, -16, -19, 20, 25],\n [-4, -21, -6, -10, 12, -16, 12, -22, 4, -11, -15, 3],\n [-2, -15, -24, -10, 26, -23, -21, 23, 21, -12, 5, -6],\n [-25, 19, 21, -24, -2, 0, 0, -4, -18, 9, -16, 12],\n [-20, -14, -20, 15, 20, 16, -14, 26, -21, -23, 16, -2],\n [-7, -18, -2, 10, -18, 14, 17, -8, -15, 8, -23, -8],\n [23, 17, 19, -21, 4, 20, 24, 5, -18, 21, -1, -21],\n [10, 16, 7, 13, 24, -6, 15, 0, 25, -8, 0, -24],\n [-2, 7, 24, -6, -16, 0, 1, -23, 17, 14, 26, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
95
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_993
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[-1, -6, 12, -23, 10, 22, 16, -23, 23, -4, -18, 13],\n [-3, 2, -20, -9, -25, 1, 16, 14, 2, 18, -10, 4],\n [-10, 4, -4, -17, -21, 11, 20, 0, -16, -7, 19, -22],\n [5, -22, -5, -26, -7, 24, -12, -16, 5, 1, 1, -10],\n [7, -3, -25, 0, -18, 25, -8, 9, 2, -16, 5, 0],\n [25, 12, -3, 0, 0, 13, 5, 18, 17, -5, 22, 15],\n [5, 21, 19, 8, -26, 26, 7, -26, 15, 8, 2, -9],\n [-21, -21, 0, 12, 26, -8, 11, -24, 26, 24, 11, -7],\n [-25, -20, -22, -2, 15, 26, -14, -15, -22, -15, -9, -24],\n [-23, 16, -8, -6, -2, -24, -20, -18, -23, -4, -16, -8],\n [-26, -23, -18, 15, -20, -1, -6, 21, -17, -17, -26, 9],\n [-24, 8, 18, -15, 0, -10, -8, -17, 16, -1, -19, 25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
93
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_994
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[12, -25, -15, 12, 13, 4, 2, -19, -12, -1, 21, 9],\n [14, -23, 23, 6, -15, 23, 26, -16, 3, 26, 18, -1],\n [23, 3, 9, 6, 18, 4, -25, -12, -25, 26, -15, -9],\n [-19, -24, 8, 6, 4, -23, -4, 10, 18, 18, 8, 13],\n [26, 11, -26, -24, -17, 25, 3, 1, -11, -23, 26, 21],\n [18, -23, -4, 13, -4, 23, -12, -14, -26, 10, -3, 17],\n [-26, 18, 23, 18, -14, 11, -10, 24, 3, -7, 15, -22],\n [14, -22, 19, 10, -11, -6, 7, 19, 23, -21, 15, -21],\n [-17, 4, -21, -24, 17, 25, -2, -7, 8, -26, 25, 4],\n [-13, -24, -11, -13, -24, -21, -18, 6, 14, -15, -25, 16],\n [19, -24, -14, 4, -18, 13, 14, -19, -5, -1, -11, 5],\n [8, 9, -26, -20, 23, 22, 13, 15, 21, -16, -16, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
590
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_995
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[14, -23, -2, -24, -17, -22, -15, 7, -15, 26, 11, -12],\n [-6, -23, -16, -17, -20, -18, -9, 20, 0, 16, 1, 5],\n [-17, 7, -22, -7, 3, 6, -8, -25, -9, -13, -22, -9],\n [18, 24, -12, -4, 23, -23, 7, -3, -15, 2, -21, -3],\n [20, -5, -10, 5, -2, 26, -1, 0, -20, 8, 7, 0],\n [-19, 8, -9, -4, 3, -11, 4, 11, 23, 7, -26, -18],\n [9, 17, -23, 18, -7, 18, -10, 17, -17, 19, 16, 13],\n [-14, 11, 17, -11, 12, 6, 0, 10, 21, -11, -12, -11],\n [-21, 2, 13, -10, 13, -20, 7, 18, 9, -1, -1, -16],\n [-2, 9, 15, 21, -25, 14, 1, -26, -21, 13, 9, -26],\n [22, -12, -26, -8, -2, -13, -5, -4, -20, 7, -16, -11],\n [20, 11, -18, -23, 18, 13, 8, -4, -3, -23, 3, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
92
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_996
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[5, 25, 11, 7, 7, 4, 4, 5, 9, -5, -8, 18],\n [8, 11, 15, -12, 11, -19, 5, 9, 10, 3, 24, 21],\n [-4, 16, -20, -5, 9, 12, 1, -15, -24, 18, 11, 17],\n [9, -6, -5, -4, -20, -20, -6, 17, -13, 15, -20, -22],\n [10, -8, -2, -15, -18, -26, 25, 16, 2, 16, -8, -12],\n [9, -9, -5, -5, 3, -20, 21, -21, -14, 25, -13, -25],\n [15, -11, 12, 19, 6, -26, 3, -16, -13, 10, 10, 26],\n [8, -13, 21, -5, 4, -9, -17, -3, -3, 5, 10, 7],\n [26, -17, 19, -13, -4, 5, 20, -15, 14, -3, 7, 20],\n [-7, 2, -11, 25, 13, 23, 15, -18, 17, 23, 25, -24],\n [-17, 13, -26, -20, 4, 14, -14, -5, -11, -5, -21, 26],\n [19, -26, -25, 0, -15, -21, -25, 10, -17, -10, -10, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
525
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_997
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-26, -7, -9, -18, 5, -10, -8, 22, -14, -26, 18, 11],\n [17, 11, 9, -17, 8, -1, 21, 6, 13, -19, -7, -25],\n [12, 13, 1, 2, 26, -2, -1, -19, 3, 25, -26, 1],\n [3, -14, 14, 22, -6, -6, 13, -16, 0, -22, -14, -15],\n [13, 6, 3, -24, 21, -4, 4, -21, -16, 10, 12, 20],\n [18, 10, 12, 24, -21, -9, -26, -9, 25, -16, 15, -21],\n [-22, -3, -25, 21, 8, 7, 15, -25, 25, -15, -25, 20],\n [23, 8, 2, 6, -22, 16, 25, 16, 6, 12, -14, 4],\n [9, -8, -2, 16, 8, 26, 10, 12, 6, 16, -24, 24],\n [20, 15, -3, -24, -20, -14, -3, 11, 3, -22, -4, 14],\n [17, 0, -9, 13, -7, -21, 3, 23, -21, 23, -10, 16],\n [26, 9, -12, 25, -10, -2, 17, 3, 16, 13, -10, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
554
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_998
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[17, 21, 21, 22, 15, 15, 8, -16, 1, 17, -7, -25],\n [14, 6, 9, -17, 18, -8, -2, 0, 8, -4, 16, 7],\n [-19, -25, -2, -18, -2, 18, 2, -5, -13, 25, 21, 16],\n [21, -16, 23, 24, 24, -14, 6, -24, 20, 25, 9, 24],\n [21, 15, 5, 9, 16, 9, 8, -22, -15, -8, 13, 0],\n [8, -17, 24, 1, 6, 20, 20, 16, 9, 8, 22, -10],\n [-16, 9, 10, -9, 4, 8, 1, -26, 4, 25, 0, 13],\n [-15, -15, 0, 0, 24, 19, -10, 25, -2, 3, -17, 13],\n [-12, -8, -23, -12, 10, -12, 6, 24, -14, -10, -8, -14],\n [-21, 13, 3, 9, 4, 26, -14, -3, 2, 22, 19, -25],\n [-11, 25, -15, 1, -1, 5, 15, -23, -22, -10, -7, 13],\n [2, -2, -9, -5, 26, -19, 13, 20, 13, -17, -10, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
527
|
math
|
train
|
math_arithmetic_matrix_svd_level_7_7_999
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[21, -7, 0, -25, 25, 2, -21, -7, 10, -8, -16, 21],\n [-9, 12, -5, 24, -13, 15, -21, -6, -19, -9, -5, -21],\n [8, 8, 19, 18, 26, -18, -11, -16, 21, -6, 15, -4],\n [18, -7, -10, 4, 25, -9, 2, 21, 5, -19, 23, -18],\n [19, -21, -22, 18, -14, -2, 4, 7, -10, -1, -7, 23],\n [-21, 5, 6, -7, 20, -16, 20, 25, -17, 16, 12, -8],\n [0, 13, 7, 9, -7, 19, -22, -17, 5, 13, 13, 1],\n [26, 2, 21, -5, -18, -25, -14, 8, 0, 3, 2, 8],\n [10, 24, -1, -23, 8, -17, -7, 22, -17, 3, -16, -11],\n [-20, -4, 13, -26, 18, -20, 14, -23, -25, -10, 13, -18],\n [-16, 17, -8, -13, -12, 20, -19, 6, -25, -25, -7, -4],\n [-9, 3, -6, 9, -24, -10, -3, 11, -23, -18, 6, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
86
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math
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train
|
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