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**worc3247** Let A be an mxn matrix with entries in $\displaystyle \mathbb{R}$. Show by using elementary row and column operations, that there are invertible matrices P and Q (where P has size $\displaystyle m \cross m$ and Q has size $\displaystyle n \cross n$) such that:

$\displaystyle PAQ=\[\left( \begin{array}{cc} I_r & 0 \\ 0 & 0 \\ \end{array} \right)\] $.

I can sort of see why this is true. You would need to use ECO's to make all but 1 entries in a row 0, and then permute the rows until you get the requied order. But I can't see how I can present this in the form of a solution. Help anyone?