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Math Help - Column Space

  1. #1
    Junior Member
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    May 2006
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    52

    Column Space

    I'm not sure how to do this. . . .

    Prove that, for any m x n matrix A and any n x p matrix B, the column space of AB is contained in the column space of A.
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  2. #2
    Junior Member
    Joined
    Nov 2005
    Posts
    39
    Here's a hint:

    If we think of any (m x n) matrix M as a linear transformation from R^n to R^m, then the column space of M is precisely the image of M... that is, if I take a column vector v in R^n, then the vector Mv in R^m always lies in the column space of M.
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