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  "body": "\n## Statement\n\nLet $A$ be a matrix. Say that a matrix $B$ is an augmentation of $A$ when $B$ is formed from $A$ by adjoining further columns to the right of $A$, so that the first columns of $B$ are the columns of $A$.\n\nIf $B$ is an augmentation of $A$, then the [[reduced row echelon form|0WF5AQYTW6]] of $B$ is an augmentation of the reduced row echelon form of $A$.\n\nIn other words, the leftmost columns of the reduced row echelon form of $B$ make up the reduced row echelon form of $A$.\n\n## Remarks\n\nThis is why one may row reduce an [[augmented matrix|0T6MWGZSXA]] and read the reduced form of the coefficient matrix from its left part.\nRow operations act on each column separately, so the added columns do not change the operations chosen for the first columns.\n",
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