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 vector $\vec{w}$ in ${\mathbb R}^3$ that is not in the image of the transformation $\vec{x}\mapsto A\vec{x}$.

$\vec{w} =$ $\left[\Rule{0pt}{3.6em}{0pt}\right.$$\left]\Rule{0pt}{3.6em}{0pt}\right.$