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  "body": "\n## Definition\n\nLet $F$ be a field.\nTake a [[system of linear equations|0GT4WWGWH2]] $Ax = b$ over $F$, with [[coefficient matrix|0HQFZAP3ND]] $A$ of size $m \\times n$ and constant vector $b \\in F^m$.\nThe *augmented matrix* of the system is the $m \\times (n+1)$ matrix $[A \\mid b]$.\nIts first $n$ columns are the columns of $A$, and its last column is $b$.\n\n## Remarks\n\nThe system $2x + y = 5$, $x - 3y = 0$ has the augmented matrix $\\left(\\begin{array}{cc|c} 2 \u0026 1 \u0026 5 \\\\ 1 \u0026 -3 \u0026 0 \\end{array}\\right)$.\n[[Elementary row operations|04XWH28452]] on the augmented matrix do not change the solution set of the system.\nMore generally, $[A \\mid B]$ denotes the matrix $A$ with the columns of a matrix $B$ added on the right.\n\n## Explanations\n\n### L1 human\n\nThe augmented matrix is the full system written as a table of numbers.\nThe vertical bar reminds us where the equals signs were.\nWe do row reduction on this table instead of rewriting the equations each time.\n",
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