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Matrixes help

  1. Nov 5, 2004 #1
    Hi all,

    I have this equation:

    ABXC = D

    Where A, B and C are regular matrixes. The task is to express the matrix X using matrixes A^-1, B^-1, C^-1, D, where A^-1 means inverse matrix.

    I don't have any idea how to solve it..

    Thank you for any help.
     
  2. jcsd
  3. Nov 5, 2004 #2

    arildno

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    Welcome to PF!
    1) Now, you know ONE property about the inverse of a matrix, for example:
    C*C^-1=C^-1*C=I
    where I is the identity matrix.
    2) You also know that for any matrix W and identity matrix I, you have:
    WI=IW=W
    3) You should also know that the product of matrices is ASSOCIATIVE, that is for matrices A, B, C, we have:
    A*B*C=(A*B)*C=A*(B*C)

    Use these properties.
     
  4. Nov 5, 2004 #3
    Thank you, I already tried to use these properties, but without success. I always end with the fact that I cannot simply move X to the right side of the equation, in order to get something like this:
    X = D / ABC, because dividing of matrix is not defined. I just need some hint. Unfortunately I'm not able to solve it using just the properties so far...
     
  5. Nov 5, 2004 #4

    arildno

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    I'll give you a start:
    1)Define the matrix W=ABX
    2) Hence, your equation can be written as:
    WC=D
    3) NOW, Apply C^-1 to this equation:
    WC*C^-1=DC^-1
    4) On your left-hand side, you may now simplify:
    W=DC^-1
    5) Or, expressed with your original matrices:
    ABX=DC^-1
    6) Can you now try to proceed further along these lines?
     
  6. Nov 5, 2004 #5
    Thank you arildno, that's exactly I was asking for - this hint (multiplicating each side with some matrix) didn't come to my mind.

    Thank you again, you helped me much!
     
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