Gauss-Jordan Elimination is 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 mulitples 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. As a method for solving simultaneous linear equations. Gauss-Jordan Elimination in fact requires more work than Gaussian eliminations followed by back substitution and so is not generally recommended.
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