2. Where in the world is Carmen Sandiego? Suppose for simplicity that she travels between New York City and Los Angeles. On any given day, if she is in NYC, there is a 40% chance she travels to LA. If she is in LA, there is a 20% chance she travels to NYC. a) It is Monday, and Carmen Sandiego is in NYC. What is the chance she will be in LA on Wednesday? (Do not use matrices.) b) It is Monday, and Carmen Sandiego is in NYC. What is the chance she will be in NYC again on Thursday? (Do not use matrices.) c) Assume Carmen Sandiego is equally likely to be in NYC or LA on Monday. Write a matrix formula for the forecast of where she will be next Monday. If you have a matrix calculator, compute it. d) If this game continues, what proportion of time does Carmen Sandiego spend in each city in the long run