Suppose $A$ is an $m \times n$ matrix, $V$ an $m \times 1$ matrix, with both $A$ and $V$ having rational entries. If the equation $A X = V$ has a solution in $\mathbb{R}^n$, then the equation has a solution with rational entries. (Here and in Question 5 below of Part $\mathrm{A}$, $\mathbb{R}^n$ is identified with the space of $n \times 1$ real matrices.)