Set A = magic(4) and t = trace(A). The scalar t should be an eigenvalue of A,

Question:

Set A = magic(4) and t = trace(A). The scalar t should be an eigenvalue of A, and the remaining eigenvalues should add up to zero. Why? Explain. Use MATLAB to verify that A - tl is singular. Compute the eigenvalues of A and a matrix X of eigenvectors. Determine the condition numbers of A and X. Is the eigenvalue problem well-conditioned? Explain. Perturb A by setting
A1 = A + 1.0e-04 * rand(4)
How do the eigenvalues of Al compare to those of A?