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

  • Thread starter LHS
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In summary, the conversation is about a diagonalizable matrix used in polynomial form and the difficulty in finding a pattern in the equations given for B^3 and B^4, leading to a request for help and a suggestion to substitute equations to solve for B2 and B4.
  • #1
LHS
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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
 
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  • #2


Can you rewrite B3 and B4?
See a pattern?
 
  • #3


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
 
  • #4


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:
  • #5


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..
 
  • #6


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?
 

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