Finding the polynomial form of a diagonalizable matrix

  • Thread starter Thread starter LHS
  • Start date Start date
Join the discussion
Registration is free. Ask a follow-up in this thread, or start your own.
Sign up Log in
5 replies · 2K views
LHS
Messages
37
Reaction score
0
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
 
Last edited by a moderator:

Discussion

Physics news on Phys.org


Can you rewrite B3 and B4?
See a pattern?
 


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
 


LHS said:

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?
 
Last edited by a moderator:


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..
 


LHS said:
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?