Chapter 12.1, Problem 1E

Find the characteristic polynomial and the eigenvalues and elgenvectors of the following symmetric matrices:

$\begin{array}{l}\text{a}\text{. }\left[\begin{array}{cc}3.5& -1.5\\ -1.5& 3.5\end{array}\right]\\ \text{b}\text{. }\left[\begin{array}{cc}0& 2\\ 2& 0\end{array}\right]\\ \text{c}\text{. }\left[\begin{array}{cc}-0.2& -2.4\\ -2.4& 1.2\end{array}\right]\\ \text{d}\text{. }\left[\begin{array}{cc}136& -48\\ -48& 164\end{array}\right]\end{array}$