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Matlab 4. In practice, techniques for finding the eigenvalues and eigenvectors of a matrix are iterative in nature. In this exercise, we will implement one such algorithm for finding the eigenvector corresponding to the eigenvalue of largest magnitude: the power method. Given a matrix A and any starting vector v(O) the power method consists of successively multiplying A with the vector and normalizing the result, A v(k-1) Algorithm 1 Power Method Initialize v(0) where liv(0)112 1 for k = 1,2 do uAv(k-1) v(k) = u/llulla end for Implement the above algorithm in matlab, stopping once either Av()-()12 Use the following code to generate the matrix A and initial vector vO). 10-6 or k500 nx - 10; ex = ones (nx, 1); Dxxspdiags ([ex -2*ex ex], [-1 0 1], nx, nx); A-kron(Dxx, speye(nx))+kron(speye (nx), Dxx); rng (2); v = rand (nx*nx, 1); v- vorm (v); Output the final vector v(k) in v. dat, the final scalar (k) in lambda. dat. and the number of iterations k in k.dat For the given matrix A, the dominant eigenvalue can be found analytically as =-8 sin where n = 10, Output the error of your computed solution |-(k)I in error, dat