Answer
$-35$
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; \[
\left[ {\begin{array}{cc}
-4 & 7 \\
1 & 7 \\
\end{array} } \right]
\] the determinant equals $-4(7)-1(7)=-35$.