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Matrix eq

  1. Dec 23, 2008 #1
    Given that A^-1 , B^-1 and C^-1 exist, solve the following equations for X:

    a)AX=C
    b)AXB=C
    c)BXA=C+B
    d)XABC=D

    plse help....
     
  2. jcsd
  3. Dec 23, 2008 #2

    HallsofIvy

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    a) Multiply both sides of the equation on the left by A-1:
    A-1AX= X= A-1C.
    b) Multiply both sides of the equation on the left by A-1 and on the right by B-1:
    A-1AXBB-1= X= A-1CB-1

    Can you try c and d now?
     
  4. Dec 23, 2008 #3
    so
    c) X=(C+B)A^-1B^-1

    d)X=B^-1C^-1D

    plse check thks
     
  5. Dec 23, 2008 #4
    c)BXA=C+B

    Therefore XA = B^(-1)(C+B) therefore X = B^(-1)(C+B)A^(-1)

    Remember matrix multiplication is NOT commutative.

    Do the same steps for d), note ORDER MATTERS
     
    Last edited: Dec 23, 2008
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