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Determinant exercise: show that

  1. May 31, 2012 #1
    Hey people, could someone solve this problem and explain step by step? It's from a past exame and I really need to know how to do it, tried everything I know (not much tho). Please don't omit steps.Really appreciated!
    imageshack.us/photo/my-images/403/dvidafrumdelgebra.png/
     
  2. jcsd
  3. May 31, 2012 #2

    Ray Vickson

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    Your link does not load. Generally, though, what you are asking here violates the PF rules. You are supposed to show us your work first, then ask for help.

    RGV
     
  4. May 31, 2012 #3

    sharks

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    Gold Member

    Just attach the picture directly to your own post. No need to use external image hosting sites.
     
  5. May 31, 2012 #4
    I think you can try finding an expression for each element of ##A_n## first. Let us call it ##x_{ijn}##

    $$ x_{ijn}=(a-b)\delta_{ij}+b $$
    $$ x_{ijn}=a\delta_{ij}+(1-\delta_{ij})b $$

    Then you can somehow show the result. Not sure how you can continue though.
     
  6. May 31, 2012 #5
    here is the atachment! Sorry but I have my examination tomorrow, I'm desesperate :s
     

    Attached Files:

  7. May 31, 2012 #6

    HallsofIvy

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    Proof by induction- if you expand each determinant, [itex]A_{n+1}[/itex], by the first row, you get a times [itex]A_n[/itex]+ n-1 times b times a subdeterminant.
     
  8. May 31, 2012 #7
    It does for me.
     
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