Question

Evaluate ${\displaystyle \left|\begin{array}{ccc}3& -2& 4\\ 2& 0& 1\\ 1& 2& 3\end{array}\right|}$

Answer 1

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

${\displaystyle =3\left|\begin{array}{cc}0& 1\\ 2& 3\end{array}\right|-(-2)\left|\begin{array}{cc}2& 1\\ 1& 3\end{array}\right|+4\left|\begin{array}{cc}2& 0\\ 1& 2\end{array}\right|}$

= 3(0 – 2) + 2(6 – 1) + 4(4 – 0)

= - 6 + 10 + 16

= 20