Answer Happy

Exercise 6 (4 points): **Create a function in a file that begins with function q-markov (P, x0) format [n,-]-size (P); q=11; The input P is an n x n matrix and the input xo is the initial state vector of the size n x 1. First, set a conditional statement to check if the given matrix P, which will have positive entries, is stochastic, that is, left-stochastic. **If P is not left-stochastic, the display a message disp('P is not a stochastic matrix') and the empty output for q will stay. **If P is left-stochastic (then it will be regular stochastic), display a message disp('P is a stochastic matrix') and, then, output the unique steady-state vector q, which is the probability vector that forms a basis for the Null space of the matrix (P-eye (n)). Employ here a MATLAB command null, 'r') to output a basis for the Null space and, then, scale the vector in the basis to get the required probability vector q. Display q with a message: disp('the steady-state vector is') q **Next, initialize k=0; and verify that the Markov chain converges to q by calculating consecutive iterations X₁ = P = x0, X₂ = P * X₁, X3 = P * X2, **To make the code simple, you can set up a "while" loop and assign each consecutive iteration to x0 again. The loop will run while the condition below holds: any (closetozeroroundoff (x0-q, 7)) Count the number of iterations k that is required to archive the required accuracy and display k in your code with a message: fprintf('number of iterations to archive required accuracy is i\n',k) Note: if x0=q, then k=0. This is the end of your function markov. **Print the function markov and closetozeroroundoff in your Live Script. **Run the function q-markov (P, x0); on the sets of variables as indicated below: %(a) P=[.6 .3;.5 .7], x0=[.4;.6] q=markov (P, x0); % (b) P=[.5 .3;.5.7],x0=[.5;.5] q=markov (P, x0); % (c) Difficulty: Easy P=[.9.2;.1.8], x0=[.11;.89] q=markov (P, x0); % (d) P=[.9.2;.1.8], x0=[.90;.10] q=markov (P, xe); %(e) P=[.90 .01 .09; .01 .90 .01;.09.09 .90], x0=[.5; 3; .2] q=markov (P, xe); 276) % (f) P=magic (5); P=P./sum (P), x0=randi (10,5,1); x0=x0./sum(x0) q=markov (P, x0); %(8) xe=q q=markov (P, x0); Note: in choice (g), the input matrix P is same as in (f) and the input vector x0 is the output q from the choice (f).