Set
C = triu(ones(4), 1) + diag([l, -1], -2)
[X, D] = eig(C)
Compute X-1CX and compare the result to D. Is C diagonalizable? Compute the rank of X and the condition number of X. If the condition number of X is large, the computed values for the eigenvalues may not be accurate. Compute the reduced row echelon form of C. Explain why 0 must be an eigenvalue of C and the corresponding eigenspace must have dimension 1. Use MATLAB to compute C4. It should equal the zero matrix. Given that C4 = O, what can you conclude about the actual values of the other three eigenvalues of C? Explain. Is C defective? Explain.