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!!