# How to find matrix A power 5 using caley hamilton theorem?

• Dec 2nd 2009, 11:42 PM
molokomesto650
How to find matrix A power 5 using caley hamilton theorem?
Hi. Im new here, so hope I can get some help. Did a search but didnt find anything on it.
Anybody can help me find Matrix A power 5 using Caley Hamilton theorem (no other option allowed here).
A=[1 1 -1
1 1 1
1 1 1]
Thanks!
• Dec 3rd 2009, 02:47 AM
mr fantastic
Quote:

Originally Posted by molokomesto650
Hi. Im new here, so hope I can get some help. Did a search but didnt find anything on it.
Anybody can help me find Matrix A power 5 using Caley Hamilton theorem (no other option allowed here).
A=[1 1 -1
1 1 1
1 1 1]
Thanks!

The first thing you need to do is get the characteristic equation. Please post those calculations.
• Dec 3rd 2009, 03:55 AM
molokomesto650
that would be (unless mistake)
- λ^3+3 λ^2-2 λ
• Dec 3rd 2009, 05:24 AM
dedust
the characteristic equation is $p(\lambda)=\lambda^3-3\lambda^2+2\lambda$

so

$A^3-3A^2+2A=0$

and

$A^5=3A^4-2A^3$
• Dec 3rd 2009, 06:38 AM
molokomesto650
thanks to both of you. Very helpful.