Answer
-59
Work Step by Step
Finding the determinant of the matrix using the rules of matrices, we find:
$$ \det \begin{pmatrix}3&4&2\\ -2&-5&4\\ 0&5&-3\end{pmatrix}\\ 3\cdot \det \begin{pmatrix}-5&4\\ 5&-3\end{pmatrix}-4\cdot \det \begin{pmatrix}-2&4\\ 0&-3\end{pmatrix}+2\cdot \det \begin{pmatrix}-2&-5\\ 0&5\end{pmatrix}\\ 3\left(-5\right)-4\cdot \:6+2\left(-10\right) \\ -59$$
