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  "body": "\n## Definition\n\nLet $F$ be a field.\nTake a [[system of linear equations|0GT4WWGWH2]] over $F$ with $m$ equations in $n$ unknowns, where equation $i$ is $a_{i1} x_1 + \\cdots + a_{in} x_n = b_i$.\nThe *coefficient matrix* of the system is the $m \\times n$ [[matrix|0VD9ZSWWJG]] $A = (a_{ij})$.\nIts entry in row $i$ and column $j$ is the coefficient of $x_j$ in equation $i$.\n\n## Remarks\n\nThe system $2x + y = 5$, $x - 3y = 0$ has the coefficient matrix $\\begin{pmatrix} 2 \u0026 1 \\\\ 1 \u0026 -3 \\end{pmatrix}$.\nWith $x = (x_1, \\dots, x_n)^T$ and $b = (b_1, \\dots, b_m)^T$, the system is $Ax = b$.\nIf $A$ is square and [[invertible|0EB9N0S33C]], the system has exactly one solution, $x = A^{-1} b$.\n\n## Explanations\n\n### L1 human\n\nThe coefficient matrix keeps only the numbers in front of the unknowns, in a rectangular table.\nEach row is one equation, and each column is one unknown.\nThis table lets us work with the whole system as one object.\n",
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