Chapter 5.8, Problem 2E

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.

2. A = $\begin{array}{l}\left[\begin{array}{cc}1.8& -.8\\ -3.2& 4.2\end{array}\right];\\ \left[\begin{array}{l}1\\ 0\end{array}\right],\left[\begin{array}{l}-5.625\\ 1\end{array}\right],\left[\begin{array}{l}-3.021\\ 1\end{array}\right],\left[\begin{array}{l}-.2601\\ 1\end{array}\right],\left[\begin{array}{l}-.2520\\ 1\end{array}\right]\end{array}$