0.80 0.15 0.70 0.90 0.20 0.10 0.05 0.10 0.05 0.05 0.05 015 CC? 0.15 b > 0.75 0.85 0.95 (3.) Write down the transition matrix T for this. (b) Find each of the following Without actually taking powers of T: (a) The (3, 2) entry of T. (b) The (3, 2) entry of T2. (0) The (1, 3) entry of T2. Be careful! (d) The smallest k such that the (5, 3) entry of T'\" is nonzeo and what that value is. (e) All (2', j) such that the (z', 3') entry of T1\" is zero for all k. (f) Explain intuitively what will happen in the long term to any initial pop- ulation distribution. Justify intuitively. This question can be answered to various degrees of detail, the most basic being - in which area(s) do the populations tend to eventually move and why