Set A = round(10 rand(6)) s = ones(6, 1) b = A s The solution of the linear system Ax =

Chapter 7, Problem 1

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Set A = round(10 rand(6)) s = ones(6, 1) b = A s The solution of the linear system Ax = b is clearly s. Solve the system using the MATLAB \ operation. Compute the error x s. (Since s consists entirely of 1s, this is the same as x 1.) Now perturb the system slightly. Set t = 1.0e12, E = rand(6) 0.5, r = rand(6, 1) 0.5 and set M = A + t E, c = b + t r Solve the perturbed system Mz = c for z. Compare the solution z to the solution of the original system by computing z1. How does the size of the perturbation in the solution compare with the size of the perturbations in A and b? Repeat the perturbation analysis with t = 1.0e04 and t = 1.0e02. Is the system Ax = b well conditioned? Explain. Use MATLAB to compute the condition number of A.