Answer
$$-6$$
Work Step by Step
We use Cramer's rule to find the determinant of the matrix. Doing this, we obtain:
$$ \det \begin{pmatrix}2&-1&1\\ 1&2&-1\\ 3&4&-3\end{pmatrix}\\ 2\cdot \det \begin{pmatrix}2&-1\\ 4&-3\end{pmatrix}-\left(-1\right)\det \begin{pmatrix}1&-1\\ 3&-3\end{pmatrix}+1\cdot \det \begin{pmatrix}1&2\\ 3&4\end{pmatrix}\\ 2\left(-2\right)-\left(-1\right)\cdot \:0+1\cdot \left(-2\right)\\ -6$$
