The coefficient matrix in Archetype B, call it $B$ here, is known to be nonsingular (see Example NM). By Theorem NMUS, the linear system $\linearsystem{B}{\vect{b}}$ has a (unique) solution for every choice of $\vect{b}$. Theorem CSCS then says that $\vect{b}\in\csp{B}$ for all $\vect{b}\in\complex{3}$. Stated differently, there is no way to build an inconsistent system with the coefficient matrix $B$, but then we knew that already from Theorem NMUS.