Chapter 12.3, Problem 1E

Find the SVD of the following symmetric matrices by hand calculation, and describe geometrically the action of the matrix on the unit circle:

$\begin{array}{l}\text{a}\text{. }\left[\begin{array}{cc}-3& 0\\ 0& 2\end{array}\right]\\ \text{b}\text{. }\left[\begin{array}{cc}0& 0\\ 0& 3\end{array}\right]\\ \text{c}\text{. }\left[\begin{array}{cc}\frac{3}{2}& -\frac{1}{2}\\ -\frac{1}{2}& \frac{3}{2}\end{array}\right]\\ \text{d}\text{. }\left[\begin{array}{cc}-\frac{3}{2}& \frac{1}{2}\\ \frac{1}{2}& -\frac{3}{2}\end{array}\right]\\ \text{e}\text{. }\left[\begin{array}{cc}0.75& 1.25\\ 1.25& 0.75\end{array}\right]\end{array}$