Exercise 5.3.18 Let A=1-1 9 0-12 (a) Using MATLAB, apply inverse iteration to A with shift ?--9, starting with 0 1 ]'. For simplicity, just form B(A 91)-1 (B - 322 EIGENVALUES AND EIGENVECTORSI inv (A-9*eye (3)) in MATLAB) and iterate with B. Some of the com- mands shown in Exercise 5.3.10 may be useful here. Use format long to view more digits of your iterates. Do at least ten iterations. (b) Use V, D] - eig(A) to get the true dominant eigenvector. Calculate the errors Ilg-ulla and ratios Ilg+1-Ulla/ll b-v112 for j = 1, 2, 3, Compute the theoretical convergence rate (from the known eigenvalues) and compare it with these ratios. Notice that we have faster convergence than we had when we applied the power method to this same matrix in Exercise 5.3.10