Definition:Elementary Row Operation

Definition

Let $\mathbf A = \left[{a}\right]_{m n}$ be an $m \times n$ matrix over a field $K$.

The following are called elementary row operations on $\mathbf A$.

For some $i, j \in \left[{1 . . m}\right]: i \ne j$:

$(1): \quad r_i \to ar_i$: For some $a \in K, a \ne 0$, multiply row $i$ of $\mathbf A$ by $a$.

$(2): \quad r_i \to r_i + ar_j$: For some $a \in K$, add $a$ times row $j$ to row $i$.

$(3): \quad r_i \leftrightarrow r_j$: Interchange rows $i$ and $j$.

Also see

• Row Equivalence