One of the following operations on the rows of a matrix:

1. (i) interchange two rows,

2. (ii) multiply a row by a non‐zero scalar,

3. (iii) add a multiple of one row to another row.

An elementary row operation can be produced by a premultiplication by the appropriate elementary matrix. Elementary row operations are applied to the augmented matrix of a system of linear equations to transform it into echelon form or reduced echelon form. Each elementary row operation corresponds to an operation on the system of linear equations that does not alter the solution set of the equations or the row space of the matrix. Commonly abbreviated to ERO.