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Rank of two matrices

  1. Nov 6, 2008 #1
    1. The problem statement, all variables and given/known data

    A is nxn
    B is nxp

    Is the rank of

    [B AB ... An-1B]

    equal to the rank of

    [AB A2B ... AnB]?

    If not, under what condition will the ranks be equal?

    3. The attempt at a solution

    I don't even know where to start. I know that both matrices should have the same number of pivots, but since this is so generalized I don't know how to learn anything about how multiplying by A would change the number of pivots!

    Can someone help me out and at least give me a hint? I've been staring at this for the longest time and just don't know what to do!

    Thanks!
     
  2. jcsd
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