How can I write information into a matrices?

Hello, I'm new here and on maths, I'm working on a project of modeling the behavior of proteins and I need to do it by using linear algebra, differential ecuations and probabilities. this is ..

We have observed that for an MD run at 42 ºC, 62% of state 1 conformations remain in

state 1 from one arbitrary time t to the next, 51% of state 2 conformations remain and so

do 54% of state 3. Moreover, we have observed also that while 13% of S1 become S2, 44%

of S2 revert to S1. Non of the S3 becomes S2 directly. We will model the evolution of the

three dierent conformational states of the protein. Let's consider that at a certain time a

given ensemble of proteins is in S1 with xn mol l-1, yn in S2 and zn in S3.

1. Write down the matrix A of the linear application underlying the time step (dt)

update (i.e., vn+1 = f(vn) where vn = (xn; yn; zn)). Do the matrix columns/rows

have a special property? Why?

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this is the first question, I want help of how break down this and start my project.

how can I convert all that information into a matrix?

Thanks in advance,