Question 1 [15 marks in total] Let 10 00 0 010 0 0 0 010 1. [5 marks] (SF) Explain why this matrix A may be a transition matrix of a Markov chain. 2. [5 marks] (SF) It is known that the characteristic polynomial of A, det (A/ - A), is 15-1. Show that A has only one real eigenvalue, namely 1. (Hint: some EMET7001 knowledge is very helpful here.) 3. [5 marks] (Challenging) Let go ( A* be the law of ro in a Markov chain To, $1, .... It, ... with transition matrix A, so o = Am is the law of at. Does a converge to A limit when / - co? Does your answer depend on to? If y, converges to the same limit no matter what up is, find that limit