Answer
20
Work Step by Step
We use Cramer's rule to find the determinant of the matrix. Doing this, we obtain:
$$ \det \begin{pmatrix}5&2&-2\\ 0&1&-1\\ 3&3&1\end{pmatrix}\\ 5\cdot \det \begin{pmatrix}1&-1\\ 3&1\end{pmatrix}-2\cdot \det \begin{pmatrix}0&-1\\ 3&1\end{pmatrix}-2\cdot \det \begin{pmatrix}0&1\\ 3&3\end{pmatrix}\\ 5\cdot \:4-2\cdot \:3-2\left(-3\right) \\ 20$$
