Find a basis for the null space of matrix A.
A = $\left[\begin{array}{ccccc} 1 &0 &-4 &4 &1\cr 0 &1 &0 &1 &0\cr 0 &0 &0 &1 &4 \end{array}\right]$

A basis is $\Bigg \lbrace$$\left[\Rule{0pt}{6em}{0pt}\right.$$\left]\Rule{0pt}{6em}{0pt}\right.$, $\left[\Rule{0pt}{6em}{0pt}\right.$$\left]\Rule{0pt}{6em}{0pt}\right.$ $\Bigg \rbrace$