Consider the n x n matrix The eigenvalues of A are A = 2 -1 -1 2 1 -1 2 = 2 COS (n+1 - j) n + 1 +1-3)) for j = 1, 2,. , n. (a) Implement the power iteration to compute the dominant eigenvalue and the correspond- ing eigenvector of A. Report computed eigenvalue and corresponding eigenvector with n = 10 and k = 100 and initial vector e = (1,0,, 0), where k is the number of iteration. (b) Implement the QR algorithm (without shift). Comment on the rate at which the off- diagonal entries in A are reduced with n = 10. (c) Implement the shift QR algorithm with the shifts Ak (n, n). Comment on the rate at which the off-diagonal entries in A are reduced with n = 10. Notes: (1) You may use MATLAB function [Q, R] =qr(A) to perform the QR factorization of A. (c) Turn in a list of your code together with the computed eigenvalue(s) and eigenvector(s).