An extension of the method of Gaussian elimination. At the stage when the i‐th row has been divided by a suitable value to obtain a 1, suitable multiples of this row are subtracted, not only from subsequent rows but also from preceding rows to produce zeros both below and above the 1. The result of this systematic method is that the augmented matrix is transformed into reduced echelon form. However, as a method for solving simultaneous linear equations, Gauss–Jordan elimination in fact requires more work than Gaussian elimination followed by backward substitution and is less numerically stable.