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Math Help - Rank of 2 matrices Proof.

  1. #1
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    Rank of 2 matrices Proof.

    Hello

    Both of the below theorems are listed as properties 6 and 7 on the wikipedia page for the rank of a matrix.

    I want to prove the following,

    If A is an M by n matrix and B is a square matrix of rank n, then rank(AB) =  rank (A) .

    Apparently this is a corollary to the theorem
    If A and B are two matrices which can be multiplied, then rank(AB) \leq  min(rank (A), rank (B)).

    which I know how to prove. But I can't prove the first theorem. Any ideas?
    Last edited by aukie; July 19th 2012 at 12:57 PM.
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  2. #2
    Super Member girdav's Avatar
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    Re: Rank of 2 matrices Proof.

    What do you assume on A? If A=0 it won't work.
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    Re: Rank of 2 matrices Proof.

    girdav, spotted and corrected typo.
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    Super Member girdav's Avatar
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    Re: Rank of 2 matrices Proof.

    You can do a reasoning using linear maps, and the fact that a bijective linear map preserves linear independence.
    Thanks from aukie
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    Re: Rank of 2 matrices Proof.

    Quote Originally Posted by girdav View Post
    You can do a reasoning using linear maps, and the fact that a bijective linear map preserves linear independence.
    Do you know of any sources of a proof?
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