Answer
$-119$
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):
$\left|\begin{array}{lll}
{a_{11}}&{a_{12}}&{a_{13}}\\
{a_{21}}&{a_{22}}&{a_{23}}\\
{a_{31}}&{a_{32}}&{a_{33}}\end{array}\right|=a_{11}\left|\begin{array}{cc}
{a_{22}}&{a_{23}}\\
{a_{32}}&{a_{33}}\end{array}\right|-a_{12}\left|\begin{array}{cc}
{a_{21}}&{a_{23}}\\
{a_{31}}&{a_{33}}\end{array}\right|+a_{13}\left|\begin{array}{cc}
{a_{21}}&{a_{22}}\\{a_{31}}&{a_{32}}\end{array}\right|$
---
$D=3\left|\begin{array}{ll}
4 & 3\\
-3 & 1
\end{array}\right|-(-9)\left|\begin{array}{ll}
1 & 0\\
8 & 4
\end{array}\right|+4\left|\begin{array}{ll}
1 & 4\\
8 & -3
\end{array}\right|$
$=3[4(1)-(-3)(0)]+9[1(1)-8(0)]+4[1(-3)-8(4)]$
$=3(4)+9(1)+4(-35)$
$=12+9-140$
$=-119$
