Please help with the following seven questions:

28. Now let S = OOH COIN Show that Q" => S as n - co. 29. Show that SY = X, for any matrix Y of the form Y = 150 - y This means that no matter how the distribution starts in Pedimaxus, if Q is applied often enough, we always end up with 100 people getting the Tribune and 50 people getting the Picayune.23. 24. 25. 26. 27. Let's assume that when Pedimaxus was founded, all 150 residents got the Tribune. (Let's call this Week 0.) This would mean \"[150] 0 Since 10% of that 150 want to switch to the Picayune, we should have that for Week 1, 135 peOple get the Tribune and 15 people get the Picayune. Show that QX in this situation is indeed \"$331 Assuming that the percentages stay the same, we can get to the subscription numbers for Week 2 by computing Q2X. How many people get each paper in Week 2? Explain why the transition matrix does what we want it to do. If the conditions do not change from week to week, then Q remains the same and we have what's known as a Stochastic Process\" because Week n's numbers are found by computing QnX. Choose a few values of n and, with the help of your classmates and calculator, nd out how many people get each paper for that week. You should start to see a pattern as n ) 00. If you didn't see the pattern, we'll help you out. Let 100 X,=[ 50]. Show that QX, = X, This is called the steady state because the number of people who get each paper didn't change for the next week. Show that Q\"X ) X3 as n > oo