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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