1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    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

    User Avatar
    Homework Helper

    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

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    No, matrices are associative, A(BC) = (A B)C, but they are not always commutative.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Matrices: Transpose and Inverse
  1. Inverses of matrices (Replies: 2)

Loading...