Solution
= Solution
{c}
The three <elementary row operations> on an $m\times n$ <real matrix> are:
* Interchange two distinct rows: $R_i\leftrightarrow R_j$.
* Multiply one row by a nonzero <real number>: $R_i\leftarrow cR_i$, with $c\ne0$.
* Add a <scalar multiple> of one row to a different row: $R_i\leftarrow R_i+cR_j$, with $i\ne j$.
Each operation changes whole rows, so it acts on every column by the same rule. Each can be undone by an <elementary row operation>.