I such that and rewrite the system so that I th equation becomes first equation. It is a simple method, as compared to full pivoting, discussed later. In full pivoting further reduction can be accomplished, however, it is more complex since it involves both row and column exchanges. For larger systems look for largest . Algorithm does not require actual row exchange in the original matrix.
First step find .
This can sometimes be ameliorated using a scaling strategy. There are a number of scaling strategies. The matrix is actually not scaled. That is, no computation on the matrix itself is involved. All that is required is to effect a comparison.