Construct a matrix A as follows: A = diag(11 : 1 : 1,1); for j = 0 : 11 A = A + diag(12
Chapter 7, Problem 9(choose chapter or problem)
Construct a matrix A as follows: A = diag(11 : 1 : 1,1); for j = 0 : 11 A = A + diag(12 j : 1 : 1, j ); end (a) Compute the eigenvalues of A and the value of the determinant of A. Use the MATLAB function prod to compute the product of the eigenvalues. How does the value of the product compare with the determinant? (b) Compute the eigenvectors of A and the condition number for the eigenvalue problem. Is the problem well conditioned? Ill conditioned? Explain. (c) Set A1 = A + 1.0e04 rand(size(A)) Compute the eigenvalues of A1. Compare them with the eigenvalues of A by computing sort(eig(A1)) sort(eig(A)) and displaying the result in format long. 1
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