Example NSLIL Null space spanned by linearly independent set, Archetype L

In Example VFSAL we previewed Theorem SSNS by finding a set of two vectors such that their span was the null space for the matrix in Archetype L. Writing the matrix as $L$, we have \begin{equation*} \nsp{L}= \spn{\set{\colvector{-1\\2\\-2\\1\\0},\,\colvector{2\\-2\\1\\0\\1}} }\end{equation*} Solving the homogeneous system $\homosystem{L}$ resulted in recognizing $x_4$ and $x_5$ as the free variables. So look in entries 4 and 5 of the two vectors above and notice the pattern of zeros and ones that provides the linear independence of the set.