The eigenvalues, eigenvectors in Question-1 needs to be calculated by hand (not by computer). Questions-1: (9 mark) A car rental company has three locations. Every customer can rent from and return their car to any of these locations. Let x(n) =[x(n), x2(n), x3 (n)] be the percentage of cars available in the i-th location at time n and A be the matrix whose i,j-entry is the probability that a customer renting a car from location j at time n-1 returns it to location i at time n. 0.3 0.4 0.5 A= 0.3 0.4 0.3 0.4 0.2 0.2 (i) (ii) Write down the equation for dynamics of the system. Solve the equation for x(n). (iii) What is the long-run percentage of the cars at each location?