  A fundamental result in linear algebra states that if a homogenous linear
equation system has only the trivial solution, then there are at most as many
variables as equations. We prove the following generalisation of this
phenomenon. If a possibly infinite homogenous linear equation system with
finitely many variables in each equation has only the trivial solution, then
there exists an injection from the variables to the equations that maps each
variable to an equation in which it appears.
