swap if necessary and solve the system, however in case of a singular matrix, some pivots can be zero which can not be fixed by mere row swaps. This imposes a problem where the elimination either breaks or gives an inconsistent result. One more problem a singular matrix produces when solving a Gaussian Elimination is that it can not solve the back substitution because to back substitute the diagonal entries of the matrix must be non-zero, i.e. . However, in case of singular matrix the result is often infinitely many solutions.

Applications