Compute
\[\begin{pmatrix} 0 & 2 & -1 \\ 3 & 0 & -3 \\ 1 & 4 & -5 \end{pmatrix} \begin{pmatrix} 3 \\ 2 \\ 2 \end{pmatrix}.\]
We have that
\[\begin{pmatrix} 0 & 2 & -1 \\ 3 & 0 & -3 \\ 1 & 4 & -5 \end{pmatrix} \begin{pmatrix} 3 \\ 2 \\ 2 \end{pmatrix} = \begin{pmatrix} (0)(3) + (2)(2) + (-1)(2) \\ (3)(3) + (0)(2) + (-3)(2) \\ (1)(3) + (4)(2) + (-5)(2) \end{pmatrix} = \boxed{\begin{pmatrix} 2 \\ 3 \\ 1 \end{pmatrix}}.\]