- #1

Mr Davis 97

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## Homework Statement

Let ##A## be an ##m \times n## matrix with rank ##m##. Prove that there exists an ##n \times m## matrix ##B## such that ##AB= I_m##

## Homework Equations

## The Attempt at a Solution

So here is how far I get. I am given that ##A## has rank ##m##. Since ##L_A(x) = Ax## is a map ##\mathbb{R}^n \rightarrow \mathbb{R}^m##, this means that ##L_A## is a surjective map.

I know that in set theory, surjective maps must have right-inverses, so I get the sense that I am on the right track. But I am not sure how to continue the proof.