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Homework Help: Matrices: Transpose and Inverse

  1. Nov 20, 2012 #1
    1. The problem statement, all variables and given/known data
    Find (X * Y-1)T - (Y * X-1)T
    When X = [3 5]
    ..............[1 2]
    and Y = [3 4]
    ...........[2 3]

    2. Relevant equations
    Inverse= 1/ad-bc [d -b]
    ........................[-c a]

    3. The attempt at a solution
    I got:
    [9 -6 ]
    [14 -9]

    But the answer is:
    [-3 -2]
    [6 3]


    I did the problem twice and got the same answer so I don't think its a simple math error, any insight as to how to solve this correctly / what I've done wrong?
     
  2. jcsd
  3. Nov 20, 2012 #2

    haruspex

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    It's rather hard to say where you've gone wrong without seeing your working. Your equations are correct.
     
  4. Nov 20, 2012 #3
    Well first I did the inverse of Y and got:
    [3 -4]
    [-2 3]

    Then I multiplied that by X and got:
    [5 7]
    [-3 -4]

    Then I transposed it and got:
    [5 -3]
    [7 -4]

    Then I did the inverse of X and got:
    [2 -5]
    [-1 3]

    Multiplied by Y and got:
    [-4 -7]
    [3 5]

    Then I transposed that and got:
    [-4 3]
    [-7 5]

    Then I subtracted the two transposed matrices to get:
    [9 -6]
    [14 -9]

    Seems coherent to me but it's very far from the right answer
     
  5. Nov 20, 2012 #4

    hotvette

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    In your second step, looks like you did Y-1*X instead of X*Y-1
     
  6. Nov 20, 2012 #5
    Oh that's right!!! I forgot the associative property is non-applicable to matrices. THanks for your help.
     
  7. Nov 20, 2012 #6

    haruspex

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    No, matrices are associative, A(BC) = (A B)C, but they are not always commutative.
     
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