I have this question and I don't understand what d) and e) are asking me and why it is a Markov Matrix.

5. Letxn+1 =Axnbe a discrete dynamical system, with the initial statex0 =

0

1

andA=

1 0.5

0 0.5

.(a) Why isAaMarkovmatrix?

(d) Write the initial statex0 as a linear combination of the eigenvectors ofA

(with the equilibrium written as in c)).(e) Write the solutionxnby calculatingxn=Anx0.