Let $$A = \left[\begin{array}{ccc} -3 &1 &12\cr -3 &3 &18\cr 5 &-3 &-24 \end{array}\right].$$ Observe that the third column of $A$ is $-3$ times the first column plus $3$ times the second column. Use this information to find a nontrivial solution to $A \mathbf{x} = \mathbf{0}$.

$\boldsymbol{x} =$ $\left[\Rule{0pt}{3.6em}{0pt}\right.$$\left]\Rule{0pt}{3.6em}{0pt}\right.$