# Proof

• April 11th 2011, 07:46 AM
keelejody
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
• April 11th 2011, 08:02 AM
alexmahone
Quote:

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
• April 11th 2011, 08:04 AM
keelejody
Hero, thanks been nagging me :)