Write a script that works with 5$5$ states, and:

Constructs a random matrix, and normalizes each row so that it is a transition matrix.

Starts from a random ($($normalized)$)$ probability distribution 0$0$

and takes 50$50$ steps =>50$=>50$

Computes the stationary distribution $$

: the normalized eigenvector of $$

with eigenvalue 1($1($numerically: closest to 1)$1)$

Checks if 50$50$

and $$

are equal to tolerance 0.001$0\mathrm{.}001$