code:

/ F(i+1)  F(i)  \   / 1 1 \ i
\ F(i)    F(i-1)/ = \ 1 0 /

Use Maple to diagonalize the right hand side matrix and find a general
formula for F(i).

Where F(0)=0, F(1)=1, F(2)=1, F(3)=2... -> 0,1,1,2,3,5,8,13,21 etc.

I'm trying to get maple to give me the general solution for the fibonacci sequence. I've solved it by hand and got this:

Where Lambda1 = (1+sqrt(5))/2 and Lambda2 = (1-sqrt(5))/2 (both eigenvalues of the 2x2 Fibonacci matrix).

I can get maple to solve for specific instances, e.g. F(2), F(9), etc. The problem is just getting maple to show a general solution like the one in the image above.

Basically I've got "A^n = P * B^n * P^-1" Where A is the 2x2 fibonacci matrix (1,1; 1,0) P is a matrix whose columns are the eigenvectors of A. And the solution F(i) is the element in the second row and the first column of the resulting matrix.

If none of my explanations made any sense, I can show you my maple file if needed.

Thanks! :toothless