Answer
$57$
Work Step by Step
For a 3x3 matrix:
\[
\left[\begin{array}{rrr}
a & b & c \\
d &e & f \\
g &h & i \\
\end{array} \right]
\]
The determinant is given by:
$D=a(ei-fh)-b(di-fg)+c(dh-eg).$
Hence here $D=5(2\cdot1-1\cdot1)-(-9)(4\cdot1-1\cdot0)+4(4\cdot1-2\cdot0)=5(1)+9(4)+4(4)=57.$
