Find formulas for the entries of , where is a positive integer.
I'm not sure how to go about this. Could someone give push me in the right direction?
Now you can set up a recursion: for a = 5, b = 2, c = -1, and d = 2. This generates the next set of a, b, c, and d.
So , , etc.
Now solve the system of recursions. (That step is beyond me, I'm afraid!)
That is not how to do it topsquark. You need to diagnolize the matrix.
Where is some invertible matrix and is a diagnol matrix. Once you do that the above equation is easy to handle.
Bring everything to power of ,
Where can be found from its eigenvectors and from its eigenvalues.
(Note, computing a power of a diagnol is easy. Just raise each diagnol entry to that exponent).