## Markov Chains

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

5. Let
xn+1 = Axn be a discrete dynamical system, with the initial state x0 =
0
1

and
A =

1 0
.5
0 0
.5

.
(a) Why is
A a Markov matrix?
(d) Write the initial state
x0 as a linear combination of the eigenvectors of A

(with the equilibrium written as in c)).
(e) Write the solution
xn by calculating xn = Anx0.