A fly is trapped in a house with three rooms - room A, room B and room C. The fly moves between the rooms in the following manner: From room A, he will next move to B or C with probability 1/2 each; from B, it will next move to A with probability 3/4 and to C with probability 1/4; from C it always goes to room A. Since this fly is a continuous-time Markov fly, it stays for a random amount of time in each room that is exponentially distributed. In particular, it stays in each of the rooms A and B for an exponential amount of time with mean 5 minutes, and in room C for an exponential amount of time with mean 4 minutes. Required:
Construct the rate matrix Q