Consider the following matrix A= 4 1 TT 1 3 -1 0 -1 -1 5 2...

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Consider the following matrix A= 4 1 TT 1 3 -1 0 -1 -1 5 2 0 0 2 4 Find the true dominant eigenvalue, A, of this matrix (e.g., you can use MATLAB's eig function). Use the Power method to approximate A until a tolerance of 10-4 is achieved or until the number of iterations exceeds 25 using x(0) = (0,1,0,0). Use the Symmetric Power method to approximate A until a tolerance of 10-4 is achieved or until the number of iterations exceeds 25 using using x(0) = (0,1,0,0). Plot the iterates from both methods as they approach A. Which method performs better? Why? Consider the following matrix A= 4 1 TT 1 3 -1 0 -1 -1 5 2 0 0 2 4 Find the true dominant eigenvalue, A, of this matrix (e.g., you can use MATLAB's eig function). Use the Power method to approximate A until a tolerance of 10-4 is achieved or until the number of iterations exceeds 25 using x(0) = (0,1,0,0). Use the Symmetric Power method to approximate A until a tolerance of 10-4 is achieved or until the number of iterations exceeds 25 using using x(0) = (0,1,0,0). Plot the iterates from both methods as they approach A. Which method performs better? Why?