Category:Elementary Row Operations

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This category contains results about Elementary Row Operations.
Definitions specific to this category can be found in Definitions/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 $j$             

Also see