Answer
$-29$
Work Step by Step
We know that for a matrix
\[
\left[\begin{array}{rr}
a & b \\
c &d \\
\end{array} \right]
\]
the determinant $D$ is given by the fomrula $D=ad-bc.$
Hence, the given matrix has
$D=(-2\cdot7)-(5\cdot3)\\
D=-14-15\\
D=-29$
