Question: 1. The matrix A = ? ? ? ? ? ? 6 1 2 2 1 1 5 2 1 2 2 2 3 1

1. The matrix A = ? ? ? ? ? ? 6 1 2 2 1 1 5 2 1 2 2 2 3 1 2 2 1 1 3 2 1 2 2 2 3 ? ? ? ? ? ? has positive eigenvalues. Use the power method to find the largest and the smallest ones, and the corresponding eigenvectors. Check whether the two eigenvectors you have computed are orthogonal.

2. Using the power method, find the eigenvalues closest to ?6 and closest to 1 for the matrix: A = ? ? ? ? ? ? 1 7 ?11 2 5 0 1 4 8 ?2 0 1 0 1 0 2 0 2 4 5 7 8 2 3 0 ? ? ? ? ? ? Also write down the MATLAB/Octave commands you used to find your answer.

1. The matrix A = ? ? ? ? ? ? 6

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