Gauss–Jordan elimination

Summary

Gauss–Jordan elimination is the variant of Gaussian elimination that continues until the matrix is in reduced row echelon form. After the forward phase gives a row echelon form, it scales each pivot row to make the pivot equal to $1$. Then it adds multiples of each pivot row to the rows above it, to make every other entry in each pivot column zero. Applied to the augmented matrix of a system, the result shows the solutions directly, with no back substitution.