Row Operations

Elementary Row Operations (ERO)

EROs are operations that can be performed on augmented matrices without modifying the solution set; in other words, you can perform as many EROs as you want and the matrix will still be equivalent to the original.

There are three EROs:

1. Interchange — swapping one row with another.
2. Scaling — multiplying all values in a row by a constant.
3. Replacement — adding a scaled row to another.

\[\begin{bmatrix} \begin{array}{ccc|c} 2 & 1 & -1 & 1 \\ 3 & 4 & 2 & 13 \\ 1 & -5 & -2 & 0 \end{array} \end{bmatrix}\]