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2x2 matrix inverse

  1. Sep 24, 2008 #1
    I need to find the inverse of a 2x2 matrix of the form [a b ; c d]

    I'm halfway there, but the algebra gets really messy. Could anyone help me out by doing the problem step by step? Thanks!
  2. jcsd
  3. Sep 24, 2008 #2


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    I'm not going to do the problem for you, but I can give you a hint... you should be find that the inverse is of the form (1/ad-bc)M(a,b,c,d), where M(a,b,c,d) is a pretty simple 2x2 matrix.
  4. Sep 24, 2008 #3
    thanks for the reply. i'm aware of the formula. in fact, i'm trying to derive the formula to prove to myself that i can do gauss jordan elimination. i just got stuck midway because the algebra gets pretty messy. here's where i am in the process:

    [ a b ; c d | 1 0 ; 0 1 ] -->
    [ a b ; (ac/c) (ad/c) | 1 0 ; 0 (a/c) ] -->
    [ a b ; 0 ((ad/c)/c) -b | -1 (a/c) ] -->

    i went a couple of steps ahead and i must not be doing something right. i'd appreciate if someone could lay it out for me on the site. thanks!
  5. Sep 24, 2008 #4


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    I don't see how you got that. Starting from the matrix above that, multiply the 2nd row by -1 and add it to the first row. See how to continue from there?

    EDIT: Please don't double-post threads. You've already posted this here:
    Last edited: Sep 24, 2008
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