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Math Help - Prove there is a matrix B

  1. #1
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    Prove there is a matrix B

    Let A be an m\times n matrix and suppose that X is an n\times p matrix such that every column of X is in the column space of A. Prove there is a matrix B such that AX=B
    [Hint: we know that the equation Ax=v has a solution if and only if v\in col(A)]

    I don't know if this is exactly how the question is meant to be said. Our Prof. made a severe typo in the original, so I'm asking him to simply rewrite the question in its intended form rather than just provide us with a quick correction (which could be easily misinterpreted).
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  2. #2
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    I've consulted a few other sources for a possible answer to this question, but I am still in need of a formulaic answer. One such answer read as this:

    "For every column b of B, you get a column solution to Ax=b.

    Assemble all of those columns x into X (in the same order that you got them from b in B). For example, the third column of X will be a solution to Ax=b, where b is the third column of B."

    How would I show this in terms of mathematical formulas? Or is that thinking the wrong way?
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