Answer
It is IMPOSSIBLE for the equation to have more than one solution.
Work Step by Step
PROOF:
$C\vec{x}=\vec{v}$ is consistent for every $\vec{v}$ in $\mathbb{R}^6$ equals $C\vec{x}$ maps $\vec{x}$ onto $\mathbb{R}^6$.
By Theorem 8 clause (i), $C$ is invertible. Also by Theorem 8 (a) and (f):
$C$ is invertible. $\leftrightarrow$ $C\vec{x}=\vec{v}$ is one-to-one mapping.
So there is only one $\vec{x}$ solution for every $\vec{v}$ in $C\vec{x}=\vec{v}$.
