Construct a random integer valued 4 x 4 matrix A. 

a. Reduce A to echelon form U with no row scaling, and 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 the se 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).