Let $$A = \left[\begin{array}{cccccc} 1 &-3 &1 &-3 &3 &5\cr 0 &0 &1 &-3 &0 &2\cr 0 &0 &0 &0 &1 &-1\cr 0 &0 &0 &0 &0 &0 \end{array}\right].$$ Describe all solutions of $A\vec{x} = \vec{0}$.

$\vec{x} = x_2$ $\left[\Rule{0pt}{7.2em}{0pt}\right.$$\left]\Rule{0pt}{7.2em}{0pt}\right.$ $+ x_4$ $\left[\Rule{0pt}{7.2em}{0pt}\right.$$\left]\Rule{0pt}{7.2em}{0pt}\right.$ $+ x_6$ $\left[\Rule{0pt}{7.2em}{0pt}\right.$$\left]\Rule{0pt}{7.2em}{0pt}\right.$.