I try to find a close form for A^k,
where k is an arbitrary interger and A is 2 by 2 matrix as the following:
A = ([[r1*X, (1-r1)*X],[1-r2,r2]]);
r1 and r2 are symbolic constants, X is a variable.
First, I run the following commands in maple:
I hope to simplyfy the entries of Z3 in the order of X, i.e.,
z11 = a0*X^3 + a1*X^2 + a2*X +a3;
z12 = ....... (the same as the above)
z21 = .......
z22 = .......
But I do not know how to do it.
I try to find a law for representations of the entries of A^k by looking at the cases k=3,4,....
Any comments and hints and help are highly appreciated.