A $3\times3$ matrix is multiplied by an unknown $3\times1$ matrix and if the result is $\mathbf{0}$ how do I compute the unknown matrix?

Question

So my question is basically how to find the numerical values of $x_1$ $x_2$ and $x_3$ in the following equation.

$$ \begin{bmatrix} -1 & -2 & -3 \\ -2 & 2 & -2 \\ 1 & 2 & 3 \\ \end{bmatrix} \begin{bmatrix} x_1 \\ x_2 \\ x_3 \\ \end{bmatrix} = \mathbf{0} $$

I can do that in basic and easy to see matrices but I couldn't be able to find the solution for this matrix.