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Linear Algebra Transition Matrix Proof

  1. Apr 23, 2014 #1
    1. The problem statement, all variables and given/known data

    Prove the following theorem:
    Suppose that B, C, and D are ordered bases for a nontrivial finite dimensional vector space V. let P be the transition matrix from B to C, and let Q be the transition matrix from C to D. Then QP is the transition matrix from B to D.

    2. Relevant equations

    For every v contained in V: P[v]B=[v]c
    For every v contained in V: Q[v]c=[v]D

    3. The attempt at a solution

    Not sure how to go about doing this proof..don't even know where to start. Any help is greatly appreciated.
     
  2. jcsd
  3. Apr 24, 2014 #2
    Write out what you think QP could look like
     
  4. Apr 24, 2014 #3
    Would it be the ith column of [bi]D?
    But I'm still not sure what that looks like
     
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