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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].
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a) Determine a real root of the equation cosx = 3x-1 correct to three decimal places using Iteration method. b) Detremine the real root of the equation logx - cosx =0 by Newton
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