20. (Markov Chain) Suppose that Carly is going out of town for a week, and asks her friend Brad to watch her cat while she is gone. The cat is a fickle creature, and spends
most of his time walking around aimlessly in Carly’s apartment. The floor plan below
shows the location of rooms and doorways in Carly’s apartment, and the letters represent
the Living Room, Dining Room, Kitchen, Bathroom and Study.

Brad spends the first day in Carly’s apartment (Whiskers gets very lonely) and theorizes a
few things about the cat.
For the purposes of this question, suppose that every 5 minutes he changes location.
He must go from the room he is in, to a room connected through one of the doorways (no
phasing through walls or teleporting allowed). In addition, he will not stay in the same
room. He will always move.
a. Suppose Brad feeds the cat in the kitchen before all of the roaming starts.
Represent this with an initial state matrix. Then Create a transition matrix to represent the probability of the cat moving from one room to the next.