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Prove Au and Av Linearly Independent

  1. Feb 15, 2009 #1
    1. The problem statement, all variables and given/known data
    Let u_1...u_n be linearly independent column vectors in R^n and A an invertible n x n matrix. Prove that the vectors Au_1...Au_n are linearly independent.


    2. Relevant equations



    3. The attempt at a solution

    It is easy to prove this using scalars and the definition of linear independence. But, then why is this relevant to invertible matrices? Is there a way to prove this using column spaces, row spaces, null spaces, etc?
     
  2. jcsd
  3. Feb 15, 2009 #2

    quasar987

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    It is not true if A is not invertible!
     
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