Answer: [M] Construct a random integer-valued 4 × 4 matrix
Chapter 5, Problem 29E(choose chapter or problem)
Problem 29E
[M] Construct a random integer-valued 4 × 4 matrix A.
a. Reduce A to echelon form U with no row scaling, and use U in formula (1) (before Example 2) to compute det A. (If A happens to be singular, start over with a new random matrix.)
b. Compute the eigenvalues of A and the product of these eigenvalues (as accurately as possible).
c. List the matrix A, and, to four decimal places, list the pivots in U and the eigenvalues of A. Compute det A with your matrix program, and compare it with the products you found in (a) and (b).
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