In my garden, rabbits eat plant seedlings. Denote the rabbit r and seedling sA population at time k by D 0.5 0.75 -0.25 1.5 Pk = and assume that Pk+1 = Apk with A = (a) (Matlab) Suppose po observe? [20] 10 (c) Suppose po = Plot Pk for k= 0,...,15 as a stacked bar graph. What do you (b) The eigenvalues of A are A = 1.25 and A = 0.75. Find corresponding eigenvectors v and v by hand. Explain why {, 2} is a basis for R consisting of eigenvectors of A. 20 and that we write the vector po as a linear combination of the eigenvectors 10 Po=C1v1 + C202 with v = D -0 v2 = Find c and C. (d) Show that p = Akpo = cdfv + 02 by computing the first few terms of the sequence and identifying the pattern for the general term. (e) Find an approximation for p for large k. (f) Calculate the eventual growth rate of the combined population of rabbits and seedlings. (g) Calculate the eventual ratio of rabbits and seedlings.