Answer
$k=-1$ or $k=-4/3$.
Work Step by Step
A matrix is singular if and only if its determinant is $0$.
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 $D=1(0\cdot (-4)-(-k)\cdot1)-k((-2)\cdot (-4)-(-k)\cdot3)+2((-2)\cdot1-0\cdot3)=1(k)-k(8+3k)+2(-2)=-3k^2-7k-4=0\\3k^2+7k+4=0\\(k+1)(3k+4)=0.$
Thus $k=-1$ or $k=-4/3$.
