Answer
$-11A+2B+5C.$
Work Step by Step
We know that for a matrix
\[
\left[\begin{array}{rrr}
a & b & c \\
d &e & f \\
g &h & i \\
\end{array} \right]
\]
the determinant, $D=a(ei-fh)-b(di-fg)+c(dh-eg).$
Hence here $D=A(1\cdot1-4\cdot3)-B(2\cdot1-4\cdot1)+C(2\cdot3-1\cdot1)=-11A+2B+5C.$