(2) [20pt] Power Method and Inverse Iteration (a) Implement the Power Method for an arbitrary matrix A Rn* and an initial vector o E R". (b) Use your code to find an eigenvector of -2 1 4 A-11, 4 1-2 starting with zo (1,2,-1)T and zo = (1,2, 1)T, Report the first 5 iterates for each of the two initial vectors. Then use MATLAB's eig(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 ERn", an initial vector o E R" (d) Use your code from (c) to calculate all eigenvectors of A. You may pick appropriate values for ? Please also hand in your code. and an initial eigenvalue guess ? E R and the initial vector as you wish (obviously not the eigenvectors themselves). Always report the first 5 iterates and explain where the sequence converges to and why. (2) [20pt] Power Method and Inverse Iteration (a) Implement the Power Method for an arbitrary matrix A Rn* and an initial vector o E R". (b) Use your code to find an eigenvector of -2 1 4 A-11, 4 1-2 starting with zo (1,2,-1)T and zo = (1,2, 1)T, Report the first 5 iterates for each of the two initial vectors. Then use MATLAB's eig(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 ERn", an initial vector o E R" (d) Use your code from (c) to calculate all eigenvectors of A. You may pick appropriate values for ? Please also hand in your code. and an initial eigenvalue guess ? E R and the initial vector as you wish (obviously not the eigenvectors themselves). Always report the first 5 iterates and explain where the sequence converges to and why