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Matrix equation

  1. Feb 15, 2012 #1
    1. The problem statement, all variables and given/known data
    How does one go from

    x = Cx + d

    to

    x = [(I − C)^(-1)]d

    in a matrix equation?


    2. Relevant equations
    x = Cx + d

    x = [(I − C)^(-1)]d

    3. The attempt at a solution
    I tried to Google.
     
  2. jcsd
  3. Feb 15, 2012 #2
    Do you need to get there using a matrix equation or just know how to get there? I know how to get to that equation without matrices. I would not know how to get there with them though. Matrices were never my strong suit.

    edit:
    http://www.youtube.com/watch?v=tuepwWQ4_mM I think you might find this helpful.
     
  4. Feb 15, 2012 #3

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    I is the identity matrix, yes? Ix=x. So write the equation as Ix=Cx+d. Can you take it from there?
     
  5. Feb 15, 2012 #4
    Think about how you'd solve this with your usual numbers
    x=ax+b
    (1-a)x=b
    x=(1-a)^-1 b
    You followin'?
     
  6. Feb 15, 2012 #5

    Mark44

    Staff: Mentor

    The equation uses matrices, so if you don't feel confident answering a question that involves matrices, you shouldn't respond.
     
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