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Let B and B' be two bases (in matrix form) for R". The following statements are true about the transition matrix from B' to B: (a) If B = I, then the transition matrix is B'-1. b If B = I, then the transition matrix is B'. (c) If B' = I, then the transition matrix is B-1. (d) If B' = I, then the transition matrix is B.For each of the folowing transition matrices. determine whether the Markov chain with that transition matrix is regular: (1} is the Markov chain whose t'arrsltion matrix whose transition matrtx is 0 1 0 0 0.2 0.8 1 0 0 regular? (Yes or No) 5 (2} Is the Markov chain whose transl'don matrix whose transition matrix is 0 l D 0.1 0.4 0.5 0 1 0 regular? (Yes or No) 5 (3) Is the Markov chain whose translon matrix whose transition matrix is 1 0 0 0.8 0 0.2 0.8 0.2 0 regular? (Yes or No) E {4} Is the Markov chain whose transition matrix whose transition matrix Is 0 l 0 08 0 02 0 1 0 regular? (Yes or No) ' 6.4.5 A chemical solution contains A molecules of type A and an equal number of molecules of type B. A reversible reaction occurs between type A and B Continuous Time Markov Chains 315 molecules in which they bond to form a new compound AB. Suppose that in any small time interval of length h, any particular unbonded A molecule will react with any particular unbonded B molecule with probability ah + o(h), where a is a reaction rate of formation. Suppose also that in any small time interval of length /, any particular AB molecule disassociates into its A and B constituents with probability Bh + o(h), where B is a reaction rate of dissolution. Let X(1) denote the number of AB molecules at time r. Model X(/) as a birth and death process by specifying the parameters