***Please answer in MATLAB*** **Create a function in MATLAB function q=markov(P,X0) The function has to perform the following: Step 1: Check whether the given matrix P is stochastic. If P is stochastic, proceed to step 2. If P is not stochastic, the program displays a message P is not a stochastic matrix and returns q=[ ]. Step 2: Find the steady-state vector q. Recall: the steady-state vector is the probability vector that is a solution of , or, equivalently, . A rational basis for the solution set of this system that contains one vector can be found as , where n is a number of rows (or, equivalently, columns) of P. To find the unique (probability vector) q, you need to scale vector Q, that is , where (the sum of entries of the column vector Q). Step 3: Verify that the Markov chain converges to q by calculating consecutive x1=P*x0, x2=P*x1 ,x3=P*x2.... . until, for the first time, norm(xk-q)<10^-7. Output the number of iterations k and the vector xk itself. Hint: You can compute xk using while loop and reassigning x0=x1 after each iteration. Then, you will need to return x1(which will be your xk after the loop terminates) and the number of iteration k (which you can find by setting a counter within the loop). **Type the function markov in your diary file. **Run the function q=markov(P,x0) on the following matrices P and vectors x0: (a) P=[0.6 0.3;0.5 0.7] and x0 =[0.4;0.6], (b) P=[0.5 0.3; 0.5 0.7] and x0 is the same as in part (a). % Write a comment if xk is the same as vector q. (c) P =[0.9 0.2; 0.1 0.8] is a migration matrix between two regions and the initial vector x0 = [0.12; 0.88]. (d) The migration matrix P is the same as in part (c) but ; x0=[0.14; 0.86]; x0=[0.86; 0.14]. % Compare the output vectors q for part (d) with the output q for part (c) and write a comment about whether the initial vector x0 has an effect on the steady-state vector q. What about the number of iterations k? Write a comment please. (e) Car rental pick-up/return matrix P = [0.90 0.01 0.09; 0.1 0.90 0.01; 0.9 0.9 0.90] between the Airport, Downtown, and Metro, and x0=[0.5;0.3;0.2]