Word Count : 457

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Let ( A = \begin{pmatrix} 1 & 6 & 1 \ 1 & 2 & 0 \ 0 & 0 & 3 \end{pmatrix} ) and the initial vector ( x^{(0)} = \begin{pmatrix} 1 \ 0 \ 0 \end{pmatrix} ). We will perform 4 iterations of the power method to approximate the largest eigenvalue and its eigenvector. Iteration 1: [ x^{(1)} = A x^{(0)} = \begin{pmatrix} 1 & 6 & 1 \ 1 & 2 & 0 \ 0 & 0 & 3 \end{pmatrix} \begin{pmatrix} 1 \ 0 \ 0 \end{pmatrix} = \begin{pmatrix} 1 \ 1 \ 0 \end{pmatrix} ] Normalize ( x^{(1)} ) by its largest component (here, 1): [ x^{(1)} \approx \begin{pmatrix} 1 _________ _____ _____ ___ _________ ___ ________ ______ ______.
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