Set S = round(10 rand(5)); S = triu(S, 1) + eye(5) S = S_ S T = inv(S) (a) The exact

Chapter 6, Problem 18

(choose chapter or problem)

Set S = round(10 rand(5)); S = triu(S, 1) + eye(5) S = S_ S T = inv(S) (a) The exact inverse of S should have integer entries. Why? Explain. Check the entries of T , using format long. Round the entries of T to the nearest integer by setting T = round(T ). Compute T S and compare with eye(5). (b) Set A = triu(ones(5), 1) + diag(1 : 5), B = S A T The matrices A and B both have the eigenvalues 1, 2, 3, 4, and 5. Use MATLAB to compute the eigenvalues of B. How many digits of accuracy are there in the computed eigenvalues? Use MATLAB to compute and compare each of the following: (i) det(A) and det(B) (ii) trace(A) and trace(B) (iii) SA2T and B2 (iv) SA1T and B1 1