Chapter 12.1, Problem 2E

Find the characteristic polynomial and the eigenvalues and eigenvectors of the following matrices:

$\begin{array}{l}\text{a}\text{. }\left[\begin{array}{cc}7& 9\\ -6& -8\end{array}\right]\\ \text{b}\text{. }\left[\begin{array}{cc}2& 6\\ 1& 3\end{array}\right]\\ \text{c}\text{. }\left[\begin{array}{cc}2.2& 0.4\\ -0.4& 0.8\end{array}\right]\\ \text{d}\text{. }\left[\begin{array}{cc}32& 45\\ -18& -25\end{array}\right]\end{array}$