Answer
There is one and only one solution.
Work Step by Step
By Theorem 8 (e) and (i):
$D$ is linear independent $\Leftrightarrow$ $\vec{x}\mapsto D\vec{x}$ is onto $\mathbb{R}^7$.
Conclusion 1: There must EXIST a solution for each $\vec{b}$ in $D\vec{x}=\vec{b}$.
Also by Theorem 8 (f):
$\vec{x}\mapsto D\vec{x}$ is one to one.
Conclusion 2: There is only ONE solution for each $\vec{b}$ in $D\vec{x}=\vec{b}$.
