Problem 3 The movement of the population between two regions of a country is described by the following transition matrix: 0.75 0.00 0.25 1.00 The interpretation is as follows. In each period, 75% of the population of Region 1 stays in Region 1, and 25% of the population of Region 1 moves into Region 2. Additionally, everyone in Region 2 stays in Region 2 and no one from Region 2 moves into Region 1. Assume that currently 64 million people live in Region 1 and 8 million people live in Region 2. Show that the two regions' populations will be equalized in two periods