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Homework Help: Finding the inverse of this matrix.

  1. Mar 6, 2012 #1
    1. The problem statement, all variables and given/known data

    Hi there I'm trying to solve this question:

    dPs5M.png

    2. Relevant equations



    3. The attempt at a solution

    I figured i should just multiply them together and show that you get the identity matrix, but I'm having trouble cancelling out some of the terms. I'm not sure if I should write them out in matrix form first or just do them as is?
     
  2. jcsd
  3. Mar 7, 2012 #2

    Mark44

    Staff: Mentor

    I haven't worked this all the way through, but your idea of multiplying the two expressions seems like the way to go.

    Here are a couple of tips that might be helpful. The 1n1n' expressions represent n x n matrices whose entries are all 1's.

    The product 1n1n' * 1n1n' works out to be n * 1n1n', which you might need to prove by induction.
     
  4. Mar 7, 2012 #3
    It says that 1n is a vector of 1's so shouldnt 11' = n?
     
  5. Mar 7, 2012 #4
    They probably mean that [itex]1_n[/itex] is a column vector. Otherwise the dimensions wouldn't agree. Indeed: [itex](1-\rho)I[/itex] would be a matrix and [itex]1_n1_n^\prime[/itex] would be a number, so you can't add them.
     
  6. Mar 7, 2012 #5

    Mark44

    Staff: Mentor

    I agree with micromass. 1n has to be a column vector.
     
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