Answer
6
Work Step by Step
By using the cofactor expansion along the first row:
$det\begin{vmatrix}
5& 2&2\\
-1 & 1 &2\\
3&0 &0
\end{vmatrix}$
$=+5\times det\begin{vmatrix}
1 &2\\
0 &0
\end{vmatrix}-2\times det\begin{vmatrix}
-1 &2\\
3&0
\end{vmatrix}+2\times det\begin{vmatrix}
-1&1\\
3&0
\end{vmatrix}$
$=5(0-0)-2(0-6)+2(0-3)$
$=0+12-6$
$=6$
