QUESTION 1 Consider a Markov chain with (one-step) transition probability matrix P= How many communicating classes does the Markov chain have? QUESTION 2 Consider a Markov chain with (one-step) transition probability matrix P= " . How many communicating classes does the Markov chain have? QUESTION 3 Consider a Markov chain with (one-step) transition probability matrix P=|9 . What is the period of state 0? (If the state is aperiodic, enter 1.)Properties of Quadrilateral Diagonals Congruent Diagonals Intersection of Name of Diagonals Bisected Diagonals Quadrilateral Yes No Both One Neither. Perpendicular Not(1 mark each) For each of the given matrices, select all decompositions that can be applied to it. You do not have to show your work for this question. 2 ) A = [61 O Diagonalization (i.e., A = PDP-1 with D diagonal) O Schur triangularization O Spectral decomposition O Singular value decomposition b ) B = 0 1.001 Diagonalization O Schur triangularization O Spectral decomposition Singular value decomposition c) C is the 75 x 75 matrix with every entry equal to 1. Diagonalization Schur triangularization O Spectral decomposition Singular value decomposition d) D = 0 1 1 Diagonalization OSchur triangularization Spectral decomposition Singular value decomposition30. This quadrilateral has 2 diagonals. This pentagon has 5 diagonals. How many diagonals does a hexagon have? How many diagonals does an octagon have? Complete the following table: Number of sides |Number of diagonals 3 2 5 5 6 7 14 8 n 20