  We give a simple proof of a recent result of Gollin and Jo\'o: if a possibly
infinite system of homogeneous linear equations $A\vec{x} = \vec{0}$, where $A
= (a_{i, j})$ is an $I \times J$ matrix, has only the trivial solution, then
there exists an injection $\phi: J \to I$, such that $a_{\phi(j), j} \neq 0$
for all $j \in J$.
