4. (25 pts) Let A=201040502 (a) Find the characteristic equation for A. (Note: it should be a cubic equation) (b) Compute the roots of the characteristic equation and find the three eigen values. If you want, you can factor it in Matlab. (c) Find the three unit eigenvectors of A. (d) Use Matlab to find the eigenvalues and unit eigenvectors of A. (e) Computer the determinant of A, or A, and show that it is the product of the eigenvalues. (f) Computer the trace of A and show that it is the sum of the eigenvalues