## Differential Equations and Linear Algebra (4th Edition)

$-35$
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 $-4(7)-1(7)=-35$.