Given the singular coefficient matrix from Archetype A, the null space is the set of solutions to the homogeneous system of equations $\homosystem{A}$, which has a solution set and null space constructed in Example HISAA as an infinite set of vectors. \begin{align*} A&=\begin{bmatrix} 1 & -1 & 2\\ 2 & 1 & 1\\ 1 & 1 & 0 \end{bmatrix} &\nsp{A}&=\setparts{\colvector{-x_3\\x_3\\x_3}}{x_3\in\complex{\null}} \end{align*}