Dear Sir/Madam:

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:

A:=matrix([[r1*X, (1-r1)*X],[1-r2,r2]]);
Z3:=A^3;
simplify(evalm(Z3),symbolic);

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,....

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Hello, I have never used Maple before and I am working on an assignment but unfortunately class ended before I could ask my professor with some help so I was hoping someone on here might be able to help me out. All I need to do is get the first equation to look like the second equation, I would use the simplify command but I cannot break apart the l(l+1), can anyone help me out?

Equation 1:


Need it to look like this:


View 3346_phy309as1.mw on MapleNet or Download 3346_phy309as1.mw
View file details

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