A matrix is in row-echelon form (ref) if:

  • All the pivot entries are equal to
  • Any row’s that consist of only s are at the bottom of the matrix
  • The pivot in each row sists in a column to the right of the column that houses the pivot in the row above it. In other words, the pivot entries sit in a staircase pattern, where they stair-step down from the upper left corner to the lower right corner of the matrix.

If a matrix is in row-echelon form, and if, in each pivot column, the pivot entry is the only non-zero entry, then the matrix is in reduced row-echelon form (rref; редуцирана горно-триъгълна форма):