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

1. ## 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!

2. 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.

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

4. the characteristic equation is $p(\lambda)=\lambda^3-3\lambda^2+2\lambda$

so

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

and

$A^5=3A^4-2A^3$

5. thanks to both of you. Very helpful.