1. (Compute the eigenvalue with the largest magnitude) Consider the symmetric ma- trix 2 1 10 1 3 1 1 A: 1 1 4 1 0 1 1 3 and let (0) = (0.5, 0.5, 0.5, 0.5) be the initial eigenvector. Find the eigenvalue with the largest absolute value starting with v (0) use the power iteration. Write down your code, and display the results for the first three iteration. (b) Can you find the eigenvalue with the second absolute value using power itera- tion? If so, write down your result for the first three iteration. (c) Apply Rayleigh quotient iteration to A starting with v(0) to find the results for the first three iterations.

Fig: 1