Answer
$19$
Work Step by Step
For any matrix \[
\left[ {\begin{array}{cc}
a & b \\
c & d \\
\end{array} } \right]
\] the determinant equals $ad-bc$. For the matrix \[
\left[ {\begin{array}{cc}
1 & 4 \\
-4 & 3 \\
\end{array} } \right]
\] the determinant equals $1(3)-(-4)(4)=19.$