Given the nonsingular coefficient matrix from Archetype B, the solution set to the homogeneous system $\homosystem{A}$ is constructed in Example HUSAB and contains only the trivial solution, so the null space of $A$ has only a single element, \begin{align*} A&=\begin{bmatrix} -7&-6&-12\\ 5&5&7\\ 1&0&4 \end{bmatrix} &\nsp{A}&=\set{\colvector{0\\0\\0}} \end{align*}