**Row echelon form (REF)**

For each non-zero row, the leading entry is to the right of the leading entry of the row above.

E.g.

Note that the leading entry 9 of the second row is to the right of the leading entry 1 of the first row.

**Reduced row echelon form (RREF)**

A row echelon form is said to be reduced, if in each of its pivot columns, the leading entry is 1 and all other entries are 0.

E.g.

**Elementary Row Operations**

1) — multiply the th row by the constant

2) — swap the th and the th row

3) — add times of the th row to the th row.

**Gaussian Elimination Summary**

Gaussian Elimination is essentially using the elementary row operations (in any order) to make the matrix to row echelon form.

**Gauss-Jordan Elimination**

After reaching row echelon form, continue to use elementary row operations to make the matrix to reduced row echelon form.