Explanation Given: The transition matrix A = [ 1 4 3 4 1 2 1 2 ] Explanation: A vector v is said to be an equilibrium vector for a transition matrix A , if the following condition holds: v A = v Let the vector v be defined as follows, so that the multiplication holds. [ v 1 v 2 ] Then, v A = v [ v 1 v 2 ] [ 1 4 3 4 1 2 1 2 ] = [ v 1 v 2 ] Simplify the left hand side to obtain [ 1 4 v 1 + 1 2 v 2 3 4 v 1 + 1 2 v 2 ] = [ v 1 v 2 ] This gives ride to the following system of equations 1 4 v 1 + 1 2 v 2 = v 1 3 4 v 1 + 1 2 v 2 = v 2 This can be simplified to − 3 4 v 1 + 1 2 v 2 = 0 3 4 v

11th Edition

ISBN: 9780321979438

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

Publisher: PEARSON

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Chapter 10.2, Problem 7E

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The equilibrium vector corresponding to the transition matrix provided.

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Chapter 10.2, Problem 6E

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Finite Mathematics (11th Edition)

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The equilibrium vector corresponding to the transition matrix provided.

Solution Summary: The author explains that a vector v is an equilibrium vector for the transition matrix A, if the following condition holds.

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