Explanation For any transition matrix of order n × n , the equation for the equilibrium vector provided a system of n equation with n variables that are the n components of the equilibrium vector. There would exist another equation for the axiom of probability that would imply that all the components of the equilibrium vector should sum to 1. This implies the system would have ( n + 1 ) equations an n variables. As, the number of equations is greater than the number of variables, the system would provide a unique and a deterministic solution. This would only happen no more than 1 equation becomes redundant

11th Edition

ISBN: 9780321979438

Author: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey

Publisher: PEARSON

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Chapter 10.2, Problem 24E

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What can be said about the number of solutions to the system VK=V if the same system, with the extra equation that the sum of the elements of V must equal 1, had exactly one solution.

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Chapter 10.2, Problem 23E

Chapter 10.2, Problem 25E

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What can be said about the number of solutions to the system V K = V if the same system, with the extra equation that the sum of the elements of V must equal 1, had exactly one solution.

Solution Summary: The author explains that there can be any number of equilibrium vectors for a transition matrix if there is no restriction on the matrix to be regular.

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What can be said about the number of solutions to the system VK=V if the same system, with the extra equation that the sum of the elements of V must equal 1, had exactly one solution.

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Chapter 10 Solutions