Answer
-12
Work Step by Step
By using the cofactor expansion along the first row:
$det\begin{vmatrix}
-4& 1&3\\
2&-2 &4\\
1&-1 &0
\end{vmatrix}$
$=+(-4)\times det\begin{vmatrix}
-2 &4\\
-1 &0
\end{vmatrix}-1\times det\begin{vmatrix}
2 &4\\
1&0
\end{vmatrix}+3\times det\begin{vmatrix}
2&-2\\
1&-1
\end{vmatrix}$
$=-4(0+4)-1(0-4)+3(-2+2)$
$=-16+4+0$
$=-12$
