Row reduction and RREF
Core study note
Current matrices scope + original explanation
Legal elementary row operations
You may swap two rows, multiply a row by a nonzero scalar, or add a scalar multiple of one row to another. These operations preserve the solution set of a linear system.
Why RREF is useful
Reduced row echelon form exposes pivots and free variables. In an augmented matrix it also reveals contradictions such as a zero coefficient row with a nonzero constant.