hi,I donnt know how to solve this question.

3. There are three ponds, each occupied by a large number of frogs. Every day, a certain fraction of the frogs from each 5 l pond migrate to one of the two neighbouring ponds according to the diagram at the right. Thus the number of frogs in each pond changes from day to day according to the following dynamical system: 0 n+1 .8 .2 .2 3511 [ll+1] = [. 1 .7 .2] [351] Zn+1 .1 . 1 .6 Zn 4042 r The eigenvalues ofthis matrix are A = 1, A = 0.6 andA = 0.5. 0.1 I 0 7 0 6 (a) Find eigenvectors for each of these eigenvalues. (b) Suppose we start [n = 0]with 100 frogs, 60 on X, 40 on Y and none on Z. Find an expression for the numbers in X, Y and Z at time n. Write separate equations for x\