Answer
$-26$
Work Step by Step
2 by 2 determinant
$D=\left|\begin{array}{ll}
a & b\\
c & d
\end{array}\right|=ad-bc$
3 by 3 determinant (cofactors of first row):
$\left|\begin{array}{lll}
{a_{11}}&{a_{12}}&{a_{13}}\\
{a_{21}}&{a_{22}}&{a_{23}}\\
{a_{31}}&{a_{32}}&{a_{33}}\end{array}\right|=a_{11}\left|\begin{array}{cc}
{a_{22}}&{a_{23}}\\
{a_{32}}&{a_{33}}\end{array}\right|-a_{12}\left|\begin{array}{cc}
{a_{21}}&{a_{23}}\\
{a_{31}}&{a_{33}}\end{array}\right|+a_{13}\left|\begin{array}{cc}
{a_{21}}&{a_{22}}\\{a_{31}}&{a_{32}}\end{array}\right|$
---
$D=4\left|\begin{array}{ll}
-1 & 0\\
-3 & 4
\end{array}\right|-(-1)\left|\begin{array}{ll}
6 & 0\\
1 & 4
\end{array}\right|+2\left|\begin{array}{ll}
6 & -1\\
1 & -3
\end{array}\right|$
$=4[-1(4)-0(-3)]+1[6(4)-1(0)]+2[6(-3)-1(-1)]$
$=4(-4)+1(24)+2(-17)$
$=-16+24-34$
$=-26$
