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Gauss-Jordan elimination

Ordinary elimination plus a backward pass, reaching RREF directly.

Gauss-Jordan elimination is ordinary Gaussian elimination with an extra backward pass: first forward-eliminate to row echelon form as usual, then, starting from the last pivot and working back, scale each pivot row so its leading entry is 1 and clear every entry above it. The result is reduced row echelon form, with no back-substitution left to do by hand.

See also

reduced row echelon form Gaussian elimination
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