Hello, I need to use a matrix to solve this but am stumped on how to do it. All I need is a little nudge to push me in the right direction. Please help. Thank you

Question

You have been hired as a consultant for Crazy Al’s Car Rentals, a new car rental agency in the city of Metropolis. Crazy Al’s Car Rentals has a total of 2500 cars that it rents from three locations within the city: A, B, c.

Your research has shown the following weekly rental and return patterns:

• 85% of customers who rent from A return their cars to A

• 10% of customers who rent from A return their cars to B

• 80% of customers who rent from B return their cars to B

• 10% of customers who rent from B return their cars to A

• 10% of customers who rent from C return their cars to A

• 5% of customers who rent from C return their cars to B

Crazy Al, the owner of Crazy Al’s Car Rentals, has hired you to determine how many of his cars should be at each of his three locations at the start of each week so that the same number of cars will be there at the end of the week (and hence at the start of the next week).

Use what you have learned about systems of equations and matrices to set up a system of equations representing this situation and solve this problem. Then prepare a brief report outlining your work, your methods, and your findings for Crazy Al.