Let $$A =\left[\begin{array}{cccc} 1 &-3 &1 &-3\cr 0 &1 &3 &5\cr -2 &8 &4 &16 \end{array}\right].$$ Find a pair of vectors $\vec{u}, \vec{v}$ in ${\mathbb R}^4$ that span the set of all $\vec{x}\in {\mathbb R}^4$ that are mapped into the zero vector by the transformation $\vec{x} \mapsto A\vec{x}$.

$\vec{u} =$ $\left[\Rule{0pt}{4.8em}{0pt}\right.$$\left]\Rule{0pt}{4.8em}{0pt}\right.$, $\vec{v} =$ $\left[\Rule{0pt}{4.8em}{0pt}\right.$$\left]\Rule{0pt}{4.8em}{0pt}\right.$.