Difficulty: Moderate Exercise 6 (4 points):
**Create a function in a file that begins with
function q-markov (P, x0)
format
n=size (P,1);
q-1);
**First, the function has to check whether the given matrix P (that will have positive entries)
is stochastic, that is, left-stochastic. If P is not left-stochastic, the program displays a message
disp('P is not a stochastic matrix')
and terminates. The empty output for a will stay.
If P is left-stochastic (then it will be regular stochastic), we will proceed with following:
**First, find 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 a MATLAB command null(,'r')
to find a basis for the Null space and, then, scale the vector in the basis to get the required
probability vector a.
**Next, verify that the Markov chain converges to q by calculating consecutive iterations:
x =P*x0, x =P*x, x, =P*X,
You can use a “while” loop here. Your loop has to terminate when, for the first time, the
output of the function closetozeroroundoff () with p=7, run on the vector of the difference
between a consecutive iteration and q, is the zero vector. Count the number of iterations k that
is required to archive this accuracy and display k in your code with the corresponding
message.
This is the end of your function markov.
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