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In linear algebra, Gauss–Jordan elimination is a version of Gaussian elimination that puts zeros both above and below each pivot element as it goes from the top row of the given matrix to the bottom. In other words, Gauss-Jordan elimination brings a matrix to reduced row echelon form, whereas Gaussian elimination takes it only as far as row echelon form. It is considerably less efficient than the two-stage Gaussian elimination algorithm. It is named in honor of Carl Friedrich Gauss and Wilhelm Jordan. Every matrix has a reduced row echelon form, and this algorithm is guaranteed to produce it.