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  "body": "\n## Definition\n\nLet $F$ be a field and let $A$ be an $m \\times n$ [[matrix|0VD9ZSWWJG]] over $F$.\nThe *leading entry* of a nonzero row of $A$ is its first nonzero entry, from the left.\nThe matrix $A$ is in *row echelon form* when these two conditions hold:\n\n1. Each zero row of $A$ is below each nonzero row of $A$.\n2. For two consecutive nonzero rows, the leading entry of the lower row is strictly to the right of the leading entry of the upper row.\n\n## Remarks\n\nThe matrix $\\begin{pmatrix} 1 \u0026 2 \u0026 3 \\\\ 0 \u0026 0 \u0026 4 \\\\ 0 \u0026 0 \u0026 0 \\end{pmatrix}$ is in row echelon form.\nSome authors also require that each leading entry is $1$.\nIn row echelon form, all the entries below a leading entry are zero.\n[[Gaussian elimination|0JVJ2WCXZH]] changes each matrix into a row echelon form by elementary row operations.\n\n## Explanations\n\n### L1 human\n\nRow echelon form looks like a staircase.\nEach nonzero row starts further to the right than the row above it, and the zero rows sit at the bottom.\nA system in this form is easy to solve from the bottom row up.\n",
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    "name": "Row echelon form",
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  "name": "Row echelon form",
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