Here is the problem I''ve been stuck on for the longest time! Suppose A is an m x n matrix of rank m. Prove that there exists an n x m matrix B with AB = Im (Identity matrix with m number of 1s on the diagonal) Any help is appreciative!

What does the rank say about the number of linearly independent column vectors of A? What space do they span? As a consequence, what vectors can be written as linear combinations of the column vectors of A? Finally, how is making linear combinations of the column vectors of A related to the matrix product AB?

syringer,

This sounds a hell of a lot like a homework problem, and you provide no evidence that you''ve done any of the work for yourself. These forums are intended to support game development projects, and blatant attempts to get answers to homework questions are not acceptable. Since your a newbie (you just registered today), I ask that you review the forum FAQ to learn what type of post is appropriate for this forum:

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Graham Rhodes
Senior Scientist
Applied Research Associates, Inc.