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  "body": "\n## Statement\n\nLet $v_1, \\dots, v_n$ be vectors in $\\mathbb{R}^m$. Let $A$ be the [[matrix|0N1MY1T0W9]] whose columns are $v_1, \\dots, v_n$.\n\nThe vectors $v_1, \\dots, v_n$ form a [[basis|0KCQ9Y3QKA]] of $\\mathbb{R}^m$ if and only if $A$ is [[row equivalent|095DDGZF16]] to the [[identity matrix|06DW9BAWB1]].\n\n## Remarks\n\nThe identity matrix is square, so row equivalence to it forces $A$ to be an $m \\times m$ matrix. Hence $n = m$. Every basis of $\\mathbb{R}^m$ has exactly $m$ vectors.\n",
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