Every year, during the March-through-September growing season, a gardener uses a chemical test to check soil condition. Depending on the outcome of the soil test, productivity for the new season can be one of three states: (1) good, (2) fair, and (3) poor. Over the year, the gardener has observed that last years soil condition impacts current years productivity. If this years soil condition is good, there is a 0.5 chance it will not change next year, and a 0.3 chance it will be fair. If this years soil condition is fair, there is a 0.5 chance it will not change next year, and a 0.4 chance it will be poor. If this years soil condition is poor, there is a 0.6 chance it will not change next year, and a 0.3 chance it will fair

.A)Compute the transition probability vector from the fair state to all other possible states after 4 season (a⁴ ).

B)Compute the transition probability vector from the fair state to all other possible states after 8 season (a⁸ ).