Chapter 5.8, Problem 4E

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.

4. A = $\begin{array}{l}\left[\begin{array}{cc}4.1& -6\\ 3& -4.4\end{array}\right];\\ \left[\begin{array}{l}1\\ 1\end{array}\right],\left[\begin{array}{l}1\\ .7368\end{array}\right],\left[\begin{array}{l}1\\ .7541\end{array}\right],\left[\begin{array}{l}1\\ .7490\end{array}\right],\left[\begin{array}{l}1\\ .7502\end{array}\right]\end{array}$