Chapter 6.5, Problem 2E

Use the method of Example 1 to find the singular value decomposition of each of the following matrices:
(a) $\left(\begin{array}{cc}1& 1\\ 2& 2\end{array}\right)$
(b) $\left(\begin{array}{cc}2& -2\\ 1& 2\end{array}\right)$
(c) $\left(\begin{array}{cc}1& 3\\ 3& 1\\ 0& 0\\ 0& 0\end{array}\right)$
(d) $\left(\begin{array}{ccc}2& 0& 0\\ 0& 2& 1\\ 0& 1& 2\\ 0& 0& 0\end{array}\right)$