**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. $latex begin{pmatrix}

0 & mathbf{1} & 7 & 2

0 & 0 & mathbf{9} & 3

0 & 0 & 0 &…

end{pmatrix}$

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. $latex begin{pmatrix}

1 & 0 & 0 & 2

0 & 1 & 0 & 3

0 & 0 & 1 & 4

end{pmatrix}$

**Elementary Row Operations**

1) $latex cR_i$ — multiply the $latex i$th row by the constant $latex c$

2) $latex R_i leftrightarrow R_j$ —…

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