Answer
$$27$$
Work Step by Step
We use Cramer's rule to find the determinant of the matrix. Doing this, we obtain:
$$ \det \begin{pmatrix}1&4&0\\ 0&-1&2\\ 3&-2&1\end{pmatrix}\\ 1\cdot \det \begin{pmatrix}-1&2\\ -2&1\end{pmatrix}-4\cdot \det \begin{pmatrix}0&2\\ 3&1\end{pmatrix}+0\cdot \det \begin{pmatrix}0&-1\\ 3&-2\end{pmatrix}\\ 27$$
