Proof

**keelejody** · April 11th 2011, 06:46 AM

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

**alexmahone** · April 11th 2011, 07:02 AM

Originally Posted by keelejody

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

**keelejody** · April 11th 2011, 07:04 AM

Hero, thanks been nagging me

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