Reduced Row Echelon Form

Compare to row echelon form, we not only eliminate numbers below the pivot, but also eliminate those above the pivot. We gets reduced row echelon form from Gauss–Jordan elimination.

\left(\begin{array}{llll} 1 & 2 & 0 & 0 \ 0 & 0 & 1 & 0 \ 0 & 0 & 0 & 1 \end{array}\right)

\left(\begin{array}{llll} 1 & 0 & 1 & 0 \ 0 & 1 & 0 & 0 \ 0 & 0 & 1 & 1 \end{array}\right)

In reduced row echelon form, all pivots are 1 with 0 above and below. Columns with pivots are called “pivot columns.”