The power method nds the largest (in absolute value) eigenvalue and eigenvector of a diagonalizable matrix A by starting with some vector on and...

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The power method finds the largest (in absolute value) eigenvalue and eigenvector ofa diagonalizable matrix A by starting with some vector on and considering wn+1 =Awn/IIAwn”, n = 1, 2,. . .. Consider the matrix 0 1 1A = 1 O 11 1 0(a) Find the eigenvectors and eigenvalues of A. (b) Using Matlab (or some other numerical tool), implement the power method withml 2 (1,0, 0), and verify that it gives a numerically convenient approach tofinding the largest eigenvalue of A and the associated eigenvector. (c) Now implement the power method with ml 2 (—2, 1, 1). What happens? Why?