Chapter 5.8, Problem 1E

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.

1. A = $\left[\begin{array}{cc}4& 3\\ 1& 2\end{array}\right];$

$\left[\begin{array}{l}1\\ 0\end{array}\right],\left[\begin{array}{l}1\\ .25\end{array}\right],\left[\begin{array}{l}1\\ .3158\end{array}\right],\left[\begin{array}{l}1\\ .3298\end{array}\right],\left[\begin{array}{l}1\\ .3326\end{array}\right]$