PageRank can be viewed as calculating the stationary distribution of a transition matrix defined by a graph. In this problem we'l investigate the differences between various ways of calculating the stationary distribution. In particular, there are two ways of calculating the stationary distribution of a transition matrix P. One is the iterative method = linn-xMoPn for some initial , and the other one is to solve the equation }). For the following probability transition matrices, first use = P to get the stationary distribution, and then show whether or not TOP" converges as n x. If it converges, show that = limnxT0P" does not depend on 0 and interpret what this means about the stationary distribution. (Hint: you may want to diagonalize P to handle P" easily.) 1/3 2/15 8/15 (a) 2/15 1/3 8/15 1/2 0 1/2 0 0 5/6 0 1/6 PageRank can be viewed as calculating the stationary distribution of a transition matrix defined by a graph. In this problem we'l investigate the differences between various ways of calculating the stationary distribution. In particular, there are two ways of calculating the stationary distribution of a transition matrix P. One is the iterative method = linn-xMoPn for some initial , and the other one is to solve the equation }). For the following probability transition matrices, first use = P to get the stationary distribution, and then show whether or not TOP" converges as n x. If it converges, show that = limnxT0P" does not depend on 0 and interpret what this means about the stationary distribution. (Hint: you may want to diagonalize P to handle P" easily.) 1/3 2/15 8/15 (a) 2/15 1/3 8/15 1/2 0 1/2 0 0 5/6 0 1/6