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Linear algebra help: Subspaces

  1. Feb 20, 2012 #1
    1. The problem statement, all variables and given/known data
    Prove that C(AB) is a subset of C(A) for matrices A,B, where C denotes column space.

    2. Relevant equations
    C(AB) = {b \in \mathbbcode{R}^m: Ax=b is consistent}

    3. The attempt at a solution
    I don't really know where to start.
  2. jcsd
  3. Feb 21, 2012 #2


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    What's the definition of a subset?
  4. Feb 21, 2012 #3


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    to make things easier suppose that A is mxn, and B is nxp. so AB is mxp.

    now..hint: suppose u is in C(AB), which means that ABx = u, for some x in Rp.

    can you think of some vector v in Rn, with Av = u?

    (what mapping do we know for sure produces a vector in Rn?)
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