Suppose someone has three sweaters, one orange, one purple, one green. if they are wearing an orange sweater one day, on the next day they wear the orange sweater with probability .1, the purple sweater with probability .3, and the green sweater with probability .6. after wearing the purple sweater, the next day they wear the orange, purple, and green sweater with probability .2, .5, and .3, respectively. lastly after wearing the green sweater, the next day they wear the orange, purple, and green sweater with probability .8,.1, and .1, respectively. • write down the probability transition matrix for the markov chain associated the sweater color. • use a computer algebra system or techniques from linear algebra to find the approximate probability of wearing a purple sweater after, say, 1000 days.