Power Method and Inverse iteration (a) Implement the Power Method for an arbitrary matrix A Elementof R ^ n times n and an initial vector x_0 elementof r ^ n (b) Use your code to find an eigenvector of A = [-2 1 4 1 1 1 4 1 -2] starting with x_0 = (1,2, -1) ^ T and x_0 = (1,2, 1) ^ T. Report the first 5 iterates for each of the two initial vectors. Then use MATLAB's (A) to examine the eigenvalues and eigenvectors of A. Where do the sequences converge to? Why do the limits not seem to be the same? (c) Implement the Inverse Power Method for an arbitrary matrix A elementof R ^ n times n, an initial vector x_0 Elementof R ^ n and an initial eigenvalue guess theta Elementof R. d) Use your code from (c) to calculate all eigenvectors of A. You may pick appropriate values for theta and the initial vector as you wish (obviously not the eigenvectors them selves). Always report the first 5 iterates and explain where the sequence converges to and why. Power Method and Inverse iteration (a) Implement the Power Method for an arbitrary matrix A Elementof R ^ n times n and an initial vector x_0 elementof r ^ n (b) Use your code to find an eigenvector of A = [-2 1 4 1 1 1 4 1 -2] starting with x_0 = (1,2, -1) ^ T and x_0 = (1,2, 1) ^ T. Report the first 5 iterates for each of the two initial vectors. Then use MATLAB's (A) to examine the eigenvalues and eigenvectors of A. Where do the sequences converge to? Why do the limits not seem to be the same? (c) Implement the Inverse Power Method for an arbitrary matrix A elementof R ^ n times n, an initial vector x_0 Elementof R ^ n and an initial eigenvalue guess theta Elementof R. d) Use your code from (c) to calculate all eigenvectors of A. You may pick appropriate values for theta and the initial vector as you wish (obviously not the eigenvectors them selves). Always report the first 5 iterates and explain where the sequence converges to and why