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  "body": "\n## Definition\n\nLet $F$ be a field and let $A$ be an $m \\times n$ [[matrix|0VD9ZSWWJG]] over $F$, with rows $R_1, \\dots, R_m$.\nAn *elementary row operation* on $A$ is one of these three operations:\n\n1. Row switching: exchange $R_i$ and $R_j$ for some $i \\ne j$.\n2. Row scaling: replace $R_i$ by $c R_i$ for some $c \\in F$ with $c \\ne 0$.\n3. Row addition: replace $R_i$ by $R_i + c R_j$ for some $i \\ne j$ and some $c \\in F$.\n\n## Remarks\n\nEach elementary row operation has an inverse operation of the same type.\nEach elementary row operation on $A$ is the same as the product $EA$ for an [[elementary matrix|01REXW3WWE]] $E$.\nElementary row operations on an [[augmented matrix|0T6MWGZSXA]] do not change the solution set of the system.\nElementary column operations have the same definition with columns in place of rows.\n\n## Explanations\n\n### L1 human\n\nThe three row operations are the moves that we make when we solve equations by hand.\nWe can swap two equations, multiply an equation by a nonzero number, or add a multiple of one equation to another.\nNone of these moves gains or loses a solution, and each move can be undone.\n",
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