The ECHELON function uses elementary row operations to reduce a matrix to row-echelon normal form, as in the following example (Graybill; 1969):

a = {3  6  9,
     1  2  5,
     2  4 10 };
e = echelon(a);
print e;

If the argument is a square matrix, then the row-echelon normal form can be obtained from the Hermite normal form by rearranging rows that are all zeros. See the HERMITE function for details about the Hermite normal form.