A sales representative for a cosmetics firm makes calls in an area with four regions. If she is in region 1 this week, then she will be in region 2 with probability \(60 \%\), or region 4 with probability \(40 \%\), next week. If she is in region 2, then she goes to one of the other three regions next week with equal probability. The same property holds if she is in region 3 this week. If she is in region 4 this week, then next week she will be in region 2 with certainty. Define a Markov chain that models her travels, and find the transition matrix and transition diagram for this chain.