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Homework Help: Inverse of the matrix of a linear transformation

  1. Jul 14, 2010 #1
    1. The problem statement, all variables and given/known data
    Let T: M22→M22 be a LT defined by T(A)=AB where
    B=[3,2
    2,1]
    Determine if T is invertible with respect to standard bases B=C={e11,e12,e21,e22}. If so, use (equation below) to find T^-1.

    2. Relevant equations

    [[T^-1 [AB]]C = [T^-1]B to C matrix [AB]B (at least I think this is the right one)

    3. The attempt at a solution

    I found:
    T= [ [3,2,0,0]’,[2,1,0,0]’,[0,0,3,2]’,[0,0,2,1]’ ]
    T^-1 = [ [-1,2,0,0]’,[2,-3,0,0]’,[0,0,-1,2]’,[0,0,2,-3]’ ]
    My TA told me I was doing this wrong and I can't figure out what to do. Can anyone help?
     
    Last edited: Jul 14, 2010
  2. jcsd
  3. Jul 15, 2010 #2

    lanedance

    User Avatar
    Homework Helper

    so if get it right, if T is invertible then
    [tex] T^{-1}(AB) = (AB)B^{-1} = A [/tex]

    so isn't it sufficent to find whether B has an inverse
     
  4. Jul 16, 2010 #3
    Much appreciated
     
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