###### Item 1.2.5.5.d

This is false. The reduced row echelon form of the augmented matrix could look like

\begin{equation*}
\left[\begin{array}{rr|r}
1 \amp 0 \amp -3 \\
0 \amp 1 \amp 4 \\
0 \amp 0 \amp 0 \\
\end{array}\right]\text{.}
\end{equation*}

In this case, there are three equations in two unknowns, and the system has exactly one solution.