Solution
= Solution
The same scalar consistency condition now has $\mathbf a\cdot\mathbf c=1$, so it reads $0=1$. Hence \b[there is no solution].
Geometrically the image of $I+\mathbf b\mathbf a^T$ is still the <plane> $\mathbf a^\perp$, while this $\mathbf c$ is outside it. Thus the failure is inconsistency, rather than a unique solution with a singular denominator.