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

Hi. I`m 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!

Originally Posted by molokomesto650

Hi. I`m 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.

that would be (unless mistake)
- λ^3+3 λ^2-2 λ

the characteristic equation is

so



and

thanks to both of you. Very helpful.