# Category:Definitions/Elementary Row Operations

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This category contains definitions related to Elementary Row Operations.
Related results can be found in Category:Elementary Row Operations.

Let $\mathbf A = \sqbrk a_{m n}$ be an $m \times n$ matrix over a field $K$.

The elementary row operations on $\mathbf A$ are operations which act upon the rows of $\mathbf A$ as follows.

For some $i, j \in \closedint 1 m: i \ne j$:

 $(\text {ERO} 1)$ $:$ $\ds r_i \to \lambda r_i$ For some $\lambda \in K_{\ne 0}$, multiply row $i$ by $\lambda$ $(\text {ERO} 2)$ $:$ $\ds r_i \to r_i + \lambda r_j$ For some $\lambda \in K$, add $\lambda$ times row $j$ to row $i$ $(\text {ERO} 3)$ $:$ $\ds r_i \leftrightarrow r_j$ Exchange rows $i$ and $j$

## Pages in category "Definitions/Elementary Row Operations"

The following 4 pages are in this category, out of 4 total.