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.