2. Every year, people move between urban (U), suburban (S), and rural (R) populations with the probabilities given in Figure 4.5.12. Figure 4.5.12. The flow between urban, suburban, and rural populations. a. Construct the stochastic matrix A describing the movement of people. b. Explain what the Perron-Frobenius theorem tells us about the existence of a steady-state vector q and the behavior of a Markov chain