Row-Echelon in matrices

a matrix is said to be in row echelon form if:

  a.) all of the leading coefficients is 1.
  b.) each of the succeeding row from the bottom has the leading coefficient of 1
  c.) if the bottom row has all zeros (consistent dependent system).

an example of a matrix in row-echelon form.

                                                   
a matrix is said to be in reduced row-echelon form if:
 a.) it is in row-echelon form.
 b.) every leading coefficient is 1 and is the only non zero entry. (besides the constant).

an example of a matrix in reduced  row-echelon form.