###### Item1.2.5.3.d

This is not possible. If there is a solution, there will always be a free variable so there will be infinitely many solutions.

\begin{equation*} \left[\begin{array}{rrrr|r} 1 \amp 0 \amp 0 \amp * \amp * \\ 0 \amp 1 \amp 0 \amp * \amp * \\ 0 \amp 0 \amp 1 \amp * \amp * \\ \end{array}\right]\text{.} \end{equation*}
in-context