1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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:


    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


    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


    Staff: Mentor

    I agree with micromass. 1n has to be a column vector.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook