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Help with Cramer's rule

  1. Sep 5, 2006 #1
    This is from a QM problem. A & B are the unknowns, k and K are given and [itex]i = \sqrt{-1}[/itex]. Use Cramer's rule to find A and show that |A|2 = 1.

    [tex]A - B = -1[/tex]
    [tex]ikA - KB = ik[/tex]

    I applied Cramer's rule to determine A:

    [tex]A = \frac{\left |\begin{array}{cc} -1 & -1 \\ ik & -K \end{array}\right|}{\left |\begin{array}{cc} 1 & -1 \\ ik & -K \end{array}\right|}[/tex]

    So, I am left with:
    [tex]A = \frac{K + ik}{-K + ik}[/tex]

    I am stuck here, because this nowhere resembles the result I want to prove. Just guide me...
  2. jcsd
  3. Sep 5, 2006 #2


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    Homework Helper

    Whats the problem? That looks correct, and it has magnitude 1.
  4. Sep 5, 2006 #3


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    Science Advisor

    You might want to put [tex]A = \frac{K + ik}{-K + ik}[/tex]
    in "standard form" by multiplying both numerator and denominator by -K- ik.
  5. Sep 6, 2006 #4
    Ah, how silly of me :biggrin:. Thanks, HallsofIvy! I got it.
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