Physicians routinely recommend a high-fiber diet that is full of roughage, or insoluble fiber, in order to keep things moving along. While this can be helpful, in some cases a high-fiber diet may actually promote intestinal infection. High-fiber diets are also high-residue diets.
The MATRIX program is designed to perform and to teach row operation algorithms on matrices. The program can work in a decimal floating-point mode in which calculations are carried out to 18 significant digits, or it can work in a fraction mode with exact rational arithmetic.
Let z be a complex number with modulus 1. Show that thefollowing matrix is unitary.In Exercises 45â48, use the result of Exercise 44 to determine a, b,and c so that A is unitary.45. 46.47. 48.In Exercises 49â52, prove the given formula, where A and B arecomplex matrices.49. 50.51. 52.53. Let A be a matrix such that Prove that iAisHermitian.54.Show that det where A is a matrix.In Exercises 55â56, assume that the result of Exercise 54 is true formatrices of any size.55. Show that 56. Prove that if A is unitary, then 57.