Explanation Given: From the given data matrix is, T = [ 0.71 0.12 0.17 0.32 0.34 0.34 0.02 0.02 0.96 ] [ S F T ] Approach: The equilibrium matrix L can be solved by following steps. 1. Create the transition matrix T . 2. Create the equilibrium matrix L . 3. Find and simplify the system of equations described by L T = L . 4. Discard any redundant equations, and include the equation x + y + z = 1 (or similar if there are more than three variables). 5. Solve the resulting system, using either the elimination method or the graphing calculator method. 6. Check your work by verifying that L T = L . Calculation: Consider the equilibrium matrix, L = [ x y z ] Find and simplify the system of equations described by L T = L as follows, [ x y z ] [ 0.71 0.12 0.17 0.32 0.34 0.34 0.02 0.02 0.96 ] = [ x y z ] Multiply the Matrix as follows, [ 0.71 x + 0.32 y + 0.02 z 0.12 x + 0.34 y + 0.02 z 0.17 x + 0.34 y + 0.96 z ] = [ x y z ] Equate both the side equations as follows, 0.71 x + 0.32 y + 0.02 z = x 0.12 x + 0.34 y + 0.02 z = y 0.17 x + 0.34 y + 0.96 z = z The above equations can be written as follows, − 0.29 x + 0.32 y + 0.02 z = 0 0.12 x − 0.66 y + 0.02 z = 0 0.17 x + 0.34 y − 0.04 z = 0 Multiply with 100 to the above equations. − 29 x + 32 y + 2 z = 0 …… ( 1 ) 12 x − 66 y + 2 z = 0 ...... ( 2 ) 17 x + 34 y − 4 z = 0 …… ( 3 ) L = [ x y z ] is a probability equation so sum of its entries must be equal to 1 that mean, x + y + z = 1 …… ( 4 ) Multiply with − 12 in equation ( 4 ) and add the results with equation ( 2 ) as follows, 12 x − 66 y + 2 z = 0 − 12 x − 12 y − 12 z = − 12

8th Edition

ISBN: 9780357425831

Author: Johnson

Publisher: CENGAGE L

See similar textbooks

Concept explainers

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear re…

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.

Videos

Question

Chapter 11.5, Problem 5E

To determine

(a)

To find:

The ultimate market shares of the three health clubs, assuming the current trends continue.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 11.5, Problem 4E

Chapter 11.5, Problem 6E

Students have asked these similar questions

On a given day, the sea level pressure is 1013.2 hPA. The temperature at 3,000 ft AMSL is given as minus 4°C. The temperature difference compared with the ISA is: Can you give me a step by step explanation ISA - 13°C ISA - 4°C (c)ISA - 10°C (d) ISA +10°C ISA is +15 Celsius Answer is -13Celsius

Find an equation of the curve that passes through the point (0, 1) and whose slope at (x, y) is 3xy.

answer the question attched

Chapter 11 Solutions

MATHEMATICS A PRACT ODYSSEY -WEBASSIGN

Ch. 11.0A - In Exercises 1-10, a find the dimensions of the...Ch. 11.0A - Prob. 2E Ch. 11.0A - Prob. 3E Ch. 11.0A - Prob. 4E Ch. 11.0A - Prob. 5E Ch. 11.0A - Prob. 6E Ch. 11.0A - Prob. 7E Ch. 11.0A - Prob. 8E Ch. 11.0A - Prob. 9E Ch. 11.0A - In Exercises 1-10, a find the dimensions of the...

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.

(a) To find: The ultimate market shares of the three health clubs, assuming the current trends continue.

Solution Summary: The author explains how the equilibrium matrix L can be solved using the elimination method or the graphing calculator method.