In a certain country, there are three political parties: The conservative Butter-side-up party
(the Uppers), the radical Butter-side-down party (the Downers), and the progressive Pitapocket
party (the Pocketeers). Recent polls show that each year, 70% of Uppers remain
Uppers, 80% of Downers remain Downers, 40% of Pocketeers remain Pocketeers. Everyone
else switches, and they divide equally among the other two parties.
(a) Write the transition matrix representing the party-switching process.
(b) In the long run, how will the people be distributed among the political parties?