Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

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


    User Avatar
    Science Advisor

    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?)
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook