Answer
$det(A)=2$
Work Step by Step
$ \begin{bmatrix}
2 & -1 & 3 \\
1 & 4 & 4 \\
1& 0 & 2
\end{bmatrix} $
$M_{11}= \begin{bmatrix}
4 &4 \\
0& 2\\
\end{bmatrix} = 4\times2-0(4)=8$
$M_{12}= \begin{bmatrix}
1 &4 \\
1& 2\\
\end{bmatrix}=1\times2-1\times4=-2$
$M_{13}= \begin{bmatrix}
1 &4 \\
1& 0\\
\end{bmatrix}= 1\times0-1\times4=-4$
To calculate the cofactors, use the cofactor definition: $C_{ij}=(-1)^{ij}\times M_{ij}$
$C_{11}=8$
$C_{12}=2$
$C_{13}=-4$
$det(A)=a_{11}C_{11}+a_{12}C_{12}+a_{13}C_{13}$
$det(A)=2\times8+(-1)\times2+3\times(-4)$
$det(A)=2$
