Using linear algebra principles for markov chain, how would I determine the equilibrium state of the the system to figure out how many DVDs would be at location P, Q, and R? A DVD rental company has three locations, which we designate as P, Q, and R. When a DVD is rented at one ofthe locations, it may be retuned to any of the three locations. Suppose that the company starts with 100 DVD'sat each location and that the weekly distribution of DVD's for each location can be summarized as follows:Weekly DistributionLocation P: 82% stay at P, 8 % go to Q, 10% go to R.Location Q: 3% go to P, 94% go to Q, 3% go to R.Location R: 7% go to P, 6% go to Q, 87% go to R.

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Answered: A DVD rental company has three…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Using linear algebra principles for markov chain, how would I determine the equilibrium state of the the system to figure out how many DVDs would be at location P, Q, and R?

A DVD rental company has three locations, which we designate as P, Q, and R. When a DVD is rented at one of
the locations, it may be retuned to any of the three locations. Suppose that the company starts with 100 DVD's
at each location and that the weekly distribution of DVD's for each location can be summarized as follows:
Weekly Distribution
Location P: 82% stay at P, 8 % go to Q, 10% go to R.
Location Q: 3% go to P, 94% go to Q, 3% go to R.
Location R: 7% go to P, 6% go to Q, 87% go to R.

Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.

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