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  "body": "\n## Definition\n\nLet $F$ be a field and let $A$ be a matrix over $F$.\nThe matrix $A$ is in *reduced row echelon form* when these three conditions hold:\n\n1. $A$ is in [[row echelon form|0VYCDGMJJJ]].\n2. The leading entry of each nonzero row is $1$.\n3. In each column that has a leading entry, all the other entries are $0$.\n\n## Remarks\n\nThe matrix $\\begin{pmatrix} 1 \u0026 2 \u0026 0 \\\\ 0 \u0026 0 \u0026 1 \\\\ 0 \u0026 0 \u0026 0 \\end{pmatrix}$ is in reduced row echelon form.\nEach matrix is [[row equivalent|006BHFWMAP]] to exactly one matrix in reduced row echelon form.\n[[Gauss–Jordan elimination|098D6FQN3N]] computes this matrix.\nThe number of nonzero rows of the reduced row echelon form of $A$ is the [[rank|0ZC9YTXZRY]] of $A$.\n\n## Explanations\n\n### L1 human\n\nReduced row echelon form is the simplest form that row operations can reach.\nEach pivot is a $1$, and it has zeros above it and below it.\nFrom this form we can read the solutions of the system directly.\n",
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