Reduced row echelon form, abbreviated RREF, is the form of a matrix that is in row echelon form, has every leading entry
equal to 1, and has each leading 1 as the only nonzero entry in its column. Gauss-Jordan
elimination reduces a matrix to RREF. Unlike row
echelon form, the RREF of a matrix is unique.
The positions of the pivot elements identify the pivot variables, while columns without pivot elements
identify the free variables. When the indices of the columns containing the pivot
elements are applied to the original matrix, the corresponding
original columns form a basis for its column
space (Piziak and Odell 1999).
