Given linear representations M_1 and M_2 of matroids over a field F, we consider the problem (denoted by ECLR), of checking if M_1 and M_2 represent the same matroid. We show that when F=Z_2, ECLR{Z_2} is complete for $\parityL$. Let M_1,M_2\in Q ^{m\times n} be two matroid linear representations given ... more >>>