1. One estimate that can be used for the condition number of a matrix is the ratio of the largest and smallest eigenvalues. In fact, for real symmetric matrices, that turns out to be exactly the condition number. (15pts) Consider the matrix 02024, 5:21:12 PM 10-20 A = -2 0 -2 5 +4 -2 (a) Perform 3 iterations of the Power method to estimate the largest eigenvalue. Begin with an initial guess of o = [1,0,0] and use infinity norm (largest absolute value) as the eigenvalue and normalization factor. (12pts) (b) Use (c) Compute the fg to compute the smallest eigenvalue. (1pts) e ratio of your estimate of the largest and the smallest eigenvalues. Compare the results with MATLAB's values for cond. (2pts)

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