Example HUSAB shows that the coefficient matrix derived from Archetype B, specifically the $3\times 3$ matrix, \begin{equation*} B=\begin{bmatrix} -7&-6&-12\\ 5&5&7\\ 1&0&4 \end{bmatrix} \end{equation*} is a nonsingular matrix since the homogeneous system, $\homosystem{B}$, has only the trivial solution.