3. (Convergence property of power methods) Let A = () Take the initial guess 90 =[34]....

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3. (Convergence property of power methods) Let A = () Take the initial guess 90 =[34]. Perform the power method by hand and explain why the sequence q fails to converge by calculating qk and Ak. 4. (Implementation of power methods) Implement the power methods (first algorithm in problem 1) in MATLAB. See details in MATLAB Grader. Use your codes to approximate the dominant eigenvalue \eigenvector of the following matrix, -1 4 0 0 4 -1 4 0 A = 0 4 -1 4 0 0 4 -1 Take initial guess qo [1000] and the tolerance to be 10-5 a. How many iterations do you observe if the method converges? b. What is your resulting eigenvalue? What is your resulting eigenvector? Power Methods 0 solutions submitted (max: 3) Implement power methods and solve problem 4 in the homework. Script 123 1 % Generate your matrix A and initial vector qe here st 4 5 LO 6 7 [1,9] pm (A, q0,1e-5) 8 9 % Write your function here. 10 11 function [1,9]=pm(A,q0, tol) 12 13 14 15 16 17 18 19 end 3. (Convergence property of power methods) Let A = () Take the initial guess 90 =[34]. Perform the power method by hand and explain why the sequence q fails to converge by calculating qk and Ak. 4. (Implementation of power methods) Implement the power methods (first algorithm in problem 1) in MATLAB. See details in MATLAB Grader. Use your codes to approximate the dominant eigenvalue \eigenvector of the following matrix, -1 4 0 0 4 -1 4 0 A = 0 4 -1 4 0 0 4 -1 Take initial guess qo [1000] and the tolerance to be 10-5 a. How many iterations do you observe if the method converges? b. What is your resulting eigenvalue? What is your resulting eigenvector? Power Methods 0 solutions submitted (max: 3) Implement power methods and solve problem 4 in the homework. Script 123 1 % Generate your matrix A and initial vector qe here st 4 5 LO 6 7 [1,9] pm (A, q0,1e-5) 8 9 % Write your function here. 10 11 function [1,9]=pm(A,q0, tol) 12 13 14 15 16 17 18 19 end