Hello. COuld you help write the Markov chain for the following example. Thank you!

Theorem 7.37: If the n x n matrix A is the transition matrix of an n-state Markov chain, then Xm+1 = AXm for m = 0, 1, 2, ... Example 7.38: A customer always eats lunch either at restaurant A or restaurant B. . The customer never eats at A two days in a row. . If the customer eats at B one day, then the next day she is three times as likely to eat at B as at A. First, we construct the probability transition matrix for the problem. A = Q Initially, the customer is equally likely to eat at either restaurant, 50 XO = 1:91-191- Calculating subsequent state vectors: X1 = 0.125 0.875 X2 = 0.21875 0.78125 0.1953125 X3 = 0.8046875 0.20117 X4 = 0.79883 Xs = 0.19971 0.80029 0.20007 X6 = 0.79993 X1 = 0.19998 0.80002 The state vectors appear to converge to the vector 0.2 0.8Exercise Best: 0/1 In the first example, what would be the probability transition matrix A if the next day she is instead 7 times as likely to eat at B as at A? A =