Then we perform row operations on the matrix. To do this, the lowest of all "ai" (i belonging to 1-4) is taken and is subtracted from each element in that row. "This will lead to at least one zero in that row" (We get multiple zeros when there are two equal elements which also happen to be the lowest in that row). This procedure is repeated for all rows. "We now have a matrix with at least one zero per row.