The Power Method is a classic numerical algorithm for determining the largest eigenvalue and eigenvector associated with a matrix A. Write a matlab function that returns the largest eigenvalue and eigenvector using the Power Method (see wikipedia) for a given matrix A. Construct the algorithm so that it always runs 100 iterations { you should not implement a stopping criteria. Do not copy others codes.

Test your algorithm on the matrix: A = [2:0; 0:2; 1:0; 0:2; 4:0; 1:3; 0:0; 1:3; 3:0] using an initial eigenvector guess of b = [1; 1; 1].