Chapter 6.4, Problem 29E

In Exercises 23—38, evaluate each determinant.

$23.\left|\begin{array}{ccc}1& 0& -1\\ 0& 2& 2\\ -1& 0& 0\end{array}\right|24.\left|\begin{array}{ccc}2& 0& \frac{1}{2}\\ 1& 0& 2\\ 4& 0& -5\end{array}\right|$

$25.\left|\begin{array}{ccc}1& 2& 3\\ 0& 3& 4\\ 0& 0& 4\end{array}\right|26.\left|\begin{array}{ccc}2& 3& 4\\ 0& -4& 6\\ 0& 0& -5\end{array}\right|$

$27.\left|\begin{array}{ccc}1& 0& 0\\ 2& 0& 0\\ 3& 4& 5\end{array}\right|28.\left|\begin{array}{ccc}-1& 0& 0\\ 3& 2& 0\\ 4& 5& -3\end{array}\right|$

$29.\left|\begin{array}{ccc}1& 6& 0\\ 2& 5& 3\\ 3& 4& 0\end{array}\right|30.\left|\begin{array}{ccc}1& 0& 2\\ 0& 5& 7\\ 3& 1& 0\end{array}\right|$

$31.\left|\begin{array}{ccc}3& 4& 1\\ 1& 4& 3\\ 4& 3& 1\end{array}\right|32.\left|\begin{array}{ccc}3& 1& -2\\ 4& 0& -4\\ 2& -1& -3\end{array}\right|$

$33.\left|\begin{array}{ccc}0& 1& 6\\ 1& 0& 4\\ 8& 3& 1\end{array}\right|34.\left|\begin{array}{ccc}0& 2& 3\\ 1& 0& 1\\ 3& 2& 0\end{array}\right|$

$35.\left|\begin{array}{ccc}a& b& 0\\ 0& a& b\\ b& 0& a\end{array}\right|36.\left|\begin{array}{ccc}0& z& y\\ z& 0& x\\ y& x& 0\end{array}\right|$

$37.\left|\begin{array}{ccc}a& b& c\\ c& a& b\\ b& c& a\end{array}\right|38.\left|\begin{array}{ccc}u& v& w\\ w& v& u\\ u& v& w\end{array}\right|$