# Matrices Help

• Oct 24th 2009, 06:20 PM
mathportfolio99
Matrices Help
Hi, so I have a pretty difficult question, at least for me:

Consider M =
[a+b.....a-b]
[a-b.....a+b]

Show that M = A + B, where A = aX and X=
[1 1]
[1 1]

and B bY and Y =
[1 -1]
[-1 1]

Then find a general expression for M^n in terms of aX and bY.
Test the validity of your general statement by using different values of a, b, and n. Discuss the scope and/or limitations of your general statement. Use an algebraic method to explain how you arrived at your general statement.

So, for my general statement I got M^n = a^nX^n + b^nY^n

I also have a feeling that n has to be a natural number..but I am not sure how to express why that is. Any help would be great!! Thanks!!
• Oct 24th 2009, 09:36 PM
mr fantastic
Quote:

Originally Posted by mathportfolio99
Hi, so I have a pretty difficult question, at least for me:

Consider M =
[a+b.....a-b]
[a-b.....a+b]

Show that M = A + B, where A = aX and X=
[1 1]
[1 1]

and B bY and Y =
[1 -1]
[-1 1]

Then find a general expression for M^n in terms of aX and bY.
Test the validity of your general statement by using different values of a, b, and n. Discuss the scope and/or limitations of your general statement. Use an algebraic method to explain how you arrived at your general statement.

So, for my general statement I got M^n = a^nX^n + b^nY^n

I also have a feeling that n has to be a natural number..but I am not sure how to express why that is. Any help would be great!! Thanks!!

This reads like an assignment question that will count towards your final grade. Please pm me to discuss this. It is MHF policy not to knowingly provide help with such questions.