# rank of matrix

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• Mar 22nd 2009, 01:17 AM
KaKa
rank of matrix
Prove that
$A$ be $m\times n$ matrix with rank $r$ iff
there is an invertible $m\times m$ matrix $X$ and an invertible $n\times n$ matrix $Y$ such that $XAY=\begin{pmatrix}I_r & 0\\0 & 0 \end{pmatrix}$, where $I_r$ is $r\times r$ identity marix.