AbstractThis paper describes a computational technique that was used for determining whether a certain matrix equation, Mx = b, had an exact solution. Here, MT was a sparse 96,208 × 40,040 integer matrix. The approach is an appropriate alternative for certain matrices when memory constraints preclude using conventional techniques. The tools used are simple and their data structures well‐suited for virtual memory computers. An important aspect of the method is to adopt different data structures to represent the matrix as the matrix changes over the course of the problem.