In Exercises 17 and 18, suppose a mouse wanders through the given maze. The mouse must move into a different room at each time step and is equally likely to leave the room through any of the available doorways.

The mouse is placed in room 2 of the maze shown.
a. Construct a transition matrix and an initial probability vector for the mouse’s travels.
b. What are the probabilities that the mouse will be in each of the rooms after 3 moves?

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1 4 3 نیا 2 5