I'm rather unsure what is going on with the last part of question c any help would be

[LHS]

Diagonalizable matrix used in polynomial form?

Homework Statement

[PLAIN]http://img163.imageshack.us/img163/4992/photo1mpl.jpg

Homework Equations

The Attempt at a Solution

I'm rather unsure what is going on with the last part of question c any help would be greatly appreciated!

I have the other parts

 

[I like Serena]

Can you rewrite B³ and B⁴?
See a pattern?

 

[LHS]

Hmm.. I'm not really seeing a pattern, so:B^3=8*B^2-9*B-18*identity(3)

and

B^4=9*B^3-19*B^2+9*B-18*identity(3)

not spotting a pattern there

 

[berkeman]

Homework Statement

[PLAIN]http://img163.imageshack.us/img163/4992/photo1mpl.jpg

Homework Equations

The Attempt at a Solution

I'm rather unsure what is going on with the last part of question c any help would be greatly appreciated!

I have the other parts

Is this from a take-home test?

 

[LHS]

no don't worry, I'm going through past exam questions and there's nothing in my notes that can help me with this one..

 

[I like Serena]

Hmm.. I'm not really seeing a pattern, so:


B^3=8*B^2-9*B-18*identity(3)

and

B^4=9*B^3-19*B^2+9*B-18*identity(3)

not spotting a pattern there

Your equations contain B².
But you have an equation for B² that you can substitute.
Can you do so?

Then for B⁴ your equation contains B³. Can you substitute the result that you just got?