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

Finite Mathematics, Books a la Carte Plus MyLab Math Access Card Package (11th Edition)

11th Edition

ISBN: 9780133886818

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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Chapter 10 Solutions

Finite Mathematics, Books a la Carte Plus MyLab Math Access Card Package (11th Edition)

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Ch. 10.1 - Prob. 11E Ch. 10.1 - Prob. 12E Ch. 10.1 - Prob. 13E Ch. 10.1 - Prob. 14E Ch. 10.1 - In Exercises and 16, write each transition diagram...Ch. 10.1 - Prob. 16E Ch. 10.1 - Prob. 17E Ch. 10.1 - Prob. 18E Ch. 10.1 - Prob. 19E Ch. 10.1 - Find the first three powers of each transition...Ch. 10.1 - Prob. 21E Ch. 10.1 - Prob. 22E Ch. 10.1 - Prob. 23E Ch. 10.1 - Prob. 24E Ch. 10.1 - Prob. 25E Ch. 10.1 - Prob. 26E Ch. 10.1 - Prob. 27E Ch. 10.1 - Insurance An insurance company classifies its...Ch. 10.1 - Insurance The difficulty with the mathematical...Ch. 10.1 - Prob. 30E Ch. 10.1 - Prob. 31E Ch. 10.1 - 32. 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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