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Math Help - Proof

  1. #1
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    Proof

    does anyone know a proof for 7b (iv)

    http://tartarus.org/gareth/maths/Vec...rs/VM_2010.pdf

    i know what its det(A-tI)=datA+...(-1)^n-1 trA t^n-1 +(-1)t^n

    well thats about as far as i got :S
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  2. #2
    MHF Contributor alexmahone's Avatar
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    Quote Originally Posted by keelejody View Post
    does anyone know a proof for 7b (iv)

    http://tartarus.org/gareth/maths/Vec...rs/VM_2010.pdf

    i know what its det(A-tI)=datA+...(-1)^n-1 trA t^n-1 +(-1)t^n

    well thats about as far as i got :S
    det\ (A^{-1}-tI)=det\ A^{-1}(I-tA)

    = (det\ A^{-1})det\ (I-tA)

    = (det\ A)^{-1}det\ [-t(A-t^{-1})]

    = (det\ A)^{-1}(-t)^ndet\ (A-t^{-1})

    = (det\ A)^{-1}(-1)^nt^ndet\ (A-t^{-1})

    QED
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  3. #3
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    Hero, thanks been nagging me
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