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Finding Matrix A

  1. Mar 9, 2012 #1
    1. The problem statement, all variables and given/known data
    (All matrices are 2x2. Sorry for the awkward formatting)

    Find Matrix A such that
    (1 -1)-1 (2 3)
    (0 1 ) = (1 2) AT



    2. Relevant equations
    A1A2...Ak=Ak-1...A2-1A1-1


    3. The attempt at a solution
    (1 -1)-1 (2 3)
    (0 1 ) = (1 2) AT

    (1 -1)-1 (2 3)-1
    (0 1 ) (1 2) = AT

    ((2 3)(1 -1))-1
    ((1 2)(0 1)) = AT

    (2 1)-1
    (1 1) =AT

    (2 1|1 0) R1-R2 (1 0|1 -1) (1 0|1 -1)
    (1 1|0 1) = (1 1|0 1) R2-R1 = (0 1|-1 2)

    AT=(1 -1)
    ___(-1 2)
    A=(1 -1)
    __(-1 2)

    The answer was supposed to be (2 -1)
    ___________________________ (-1 1)
     
  2. jcsd
  3. Mar 9, 2012 #2
    ABA-1 ≠ B
    So for the LHS, you should put [itex]\left(^{2 3}_{1 2}\right)[/itex]-1 on the left.
     
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