When operations are to be performed on the same elementary row in a specific matrix, the columns of the two matrices are appended forming an augmented matrix. Three-row operations are usually performed on the augmented matrix to yield the system equations. The three elementary operations are; switching any two rows, multiplying a row by a constant and adding one row to another.

When switching any two rows we obtain the following:

When multiplying a row with a constant we obtain the following:

While when multiplying a row with a constant we obtain the following: