I am doing some independent studying, and came across one note from a professor, which states that if $A$ is an $m \times n$ matrix with zero nullspace, $m \geq n$. I simply have no idea on how to prove it. Hopefully someone can help me out. Thank you.
Left inverse and nullspace
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linear-algebra
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1Do you know what a contrapositive is? Can you show that if $m\lt n$ then the nullspace is nontrivial? – 2011-05-18
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0Sorry, did not know the imperative form would be that offensive and did not mean to order anyone. It is my first time here :( I tried by contradiction as Arturo mentioned but could not get the conclusion that the nullspace is nontrivial. And this is not a homework question. I will restate that later then, thanx! – 2011-05-18
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1@heber: Perhaps, now that you know that it is considered *very impolite* to post the way you did, you would be willing to edit your post to make it more polite? Also: I did *not* say "contradiction", I said [contrapositive](http://en.wikipedia.org/wiki/Contraposition). They are not the same thing. Do you know anything about systems of linear equations in which there are more equations than unknowns? – 2011-05-18