l. The Galapagos penguin is the only penguin species found north of the equator, and i1. is considered endangered. The population of the Galapagos penguin changes on a yearly basis as a discrete dynamic system. Suppose that initially there are 4!} chicks and Ill) breeding adults, that is a?" [13:]. Suppose also that the yearly transition matrix is A ] U. 2 ] (1.125 [L75 (a) \Vhich entry in the transition matrix gives the annual hirthrate of chicks per adult? 1Which entry tells us the proportion of chicks that will survive to become adults? [1 marks] (h) Calculate the state vector .73]. [0.5 marks] (9) Find the eigeuvalum and {nirresptmdiug eigemecters fer matrix A. [l marks] (d) Express In as a linear combination of cigenvectors. [1 marks] (c) Find the longterm distribution, after u years. State the long term ratio of chicks to adults. [1 tnarks] {f} From your result to part [c], is the Galapagos penguin likely to survive? [(1.5 marks]