If A runs the advertising campaign for 3 weeks, find the probability of a customer patronizing each business in the third week.
A local business A has two competitors, B and C. No customer patronizes more than one of these businesses at the same time. Initially the probabilities that a customer patronizes A, B, or C are 0.2, 0.6, and 0.2, respectively. Suppose A initiates an advertising campaign to improve its business and finds the following transition matrix to describe the effect.

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Last week's' This week's customers customers go to A B went to 0.7 A 0.2 0.1 0.4 0.4 0.2 0.4 0.4 0.2