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Homework Help: Hi,I have:AX + X = B, all of them being matrices. I have the

  1. Aug 9, 2011 #1
    Hi,

    I have:

    AX + X = B, all of them being matrices. I have the numbers in the A and B matrices and I have to find the exact values of a,b,c,d (numbers in the X matrix)

    I wanted to check if my method is correct:

    I multiplied both sides by A-1.

    2X = A-1B

    So my values for abcd would be half of the matrix I get when I multiply A-1 by B:

    Thanks,
    Peter G.
     
  2. jcsd
  3. Aug 9, 2011 #2
    Re: Matrices

    That's not quite right. We'd have

    [tex] AX +X = (A+I)X =B,[/tex]

    so if A+I were invertible then [itex] X = (A+I)^{-1}B[/itex].
     
  4. Aug 9, 2011 #3

    Mark44

    Staff: Mentor

    Re: Matrices

    To elaborate on what stringy said, here is apparently what you did:
    AX + X = B
    A-1AX + X = A-1B
    X + X = A-1B
    2X = A-1B

    Step 2 above is incorrect - you didn't multiply the entire left side of the equation by A-1.
     
  5. Aug 9, 2011 #4
    Re: Matrices

    Hey guys,

    Thanks a lot for the help. Impressive how the "Matrix World" can make me commit mistakes I probably wouldn't in the "Real Number World" :redface:

    Thanks,
    Peter
     
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