Matrix M Formulation for Xn and Xn+1

[n0_3sc]

I need help finding the form of the matrix M, here's the question:
(n and n+1 is a subscript):

Xn =
[An]
[Bn]

Xn+1 = MXn

M is a 2 x 2 matrix. The question says - What is the precise form of the matrix M?

 

[HallsofIvy]

You are going to need more information than that! For one thing, are A_n and B_n numbers? The real information you need is some definition of x_n. Just "x_n+1= Mx_n isn't enough. Do you have formulas for A_n and B_n?

 

[n0_3sc]

o sorry, the other information given is that the vectors with two components are A, & B so yes they are numbers. (which represents the concentration of a reactant-for the question).
After one time step (where n represents the timesteps thus n+1) 80% of A is transformed into B while 60% of B is tranformed into A.

Does this help?

 

[HallsofIvy]

So A_n+1= 0.2A_n+ 0.6B_n (the 20% of A left over after 80% is transformed into B and the 60% of B that is transformed into A) and
B_n+1= 0.8A_n+ 0.4B_n.

Looks like M=
[0.2 0.6]
[0.8 0.4]