Chapter 5.8, Problem 3E

In Exercises 1–4, the matrix A is followed by a sequence {x_k} produced by the power method. Use these data to estimate the largest eigenvalue of A, and give a corresponding eigenvector.

3. A = $\begin{array}{l}\left[\begin{array}{cc}.5& .2\\ .4& .7\end{array}\right];\\ \left[\begin{array}{l}1\\ 0\end{array}\right],\left[\begin{array}{l}1\\ 8\end{array}\right],\left[\begin{array}{l}.6875\\ 1\end{array}\right],\left[\begin{array}{l}.5577\\ 1\end{array}\right],\left[\begin{array}{l}.5188\\ 1\end{array}\right]\end{array}$