Question

Find the determinant:
$A=\left|\begin{array}{ccc}1& -5& 2\\ 3& 4& 1\\ 2& 3& -1\end{array}\right|$

Answer 1

$A=\left|\begin{array}{ccc}1& -5& 2\\ 3& 4& 1\\ 2& 3& -1\end{array}\right|$

$=1\left|\begin{array}{cc}4& 1\\ 3& -1\end{array}\right|+5\left|\begin{array}{cc}3& 1\\ 2& -1\end{array}\right|+2\left|\begin{array}{cc}3& 4\\ 2& 3\end{array}\right|$

$=1(-4-3)+5(-3-2)+2(9-8)$

$=-7-25+2$

$=-30$