Chapter 2.2, Problem 3E

For each of the following, compute the determinate and state whether the matrix is singular or nonsingular:

(a) $\left[\begin{array}{cc}3& 1\\ 6& 2\end{array}\right]$ (b) $\left[\begin{array}{cc}3& 1\\ 4& 2\end{array}\right]$ (c) $\left[\begin{array}{ccc}3& 3& 1\\ 0& 1& 2\\ 0& 2& 3\end{array}\right]$ (d) $\left[\begin{array}{ccc}2& 1& 1\\ 4& 3& 5\\ 2& 1& 2\end{array}\right]$ (e) $\left[\begin{array}{ccc}2& -1& 3\\ -1& 2& -2\\ 1& 4& 0\end{array}\right]$ (f) $\left[\begin{array}{cccc}1& 1& 1& 1\\ 2& -1& 3& 2\\ 0& 1& 2& 1\\ 0& 0& 7& 3\end{array}\right]$