Explanation Given: The given matrix is, T = [ 0.4 0.3 0.3 0.2 0.7 0.1 0.3 0.3 0.4 ] 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 ] [ 0.4 0.3 0.3 0.2 0.7 0.1 0.3 0.3 0.4 ] = [ x y z ] Multiply the Matrix as follows, [ 0.4 x + 0.2 y + 0.3 z 0.3 x + 0.7 y + 0.3 z 0.3 x + 0.1 y + 0.4 z ] = [ x y z ] Equate both the side equations as follows, 0.4 x + 0.2 y + 0.3 z = x 0.3 x + 0.7 y + 0.3 z = y 0.3 x + 0.1 y + 0.4 z = z The above equations can be written as follows, − 0.6 x + 0.2 y + 0.3 z = 0 0.3 x − 0.3 y + 0.3 z = 0 0.3 x + 0.1 y − 0.6 z = 0 Multiply with 10 on the above equations. − 6 x + 2 y + 3 z = 0 …… ( 1 ) 3 x − 3 y + 3 z = 0 ..... To determine (b) To verify: The solution L T = L .

MATHEMATICS A PRACTICAL ODYSSEY W/ACCESS

8th Edition

ISBN: 9780357537343

Author: Johnson

Publisher: CENGAGE L

See similar textbooks

Videos

Question

Chapter 11.5, Problem 2E

To determine

(a)

To find:

The equilibrium matrix L by solving LT=L for L.

To determine

(b)

To verify:

The solution LT=L.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 11.5, Problem 1E

Chapter 11.5, Problem 3E

Students have asked these similar questions

Solve questions

Patterns in Floor Tiling A square floor is to be tiled with square tiles as shown. There are blue tiles on the main diagonals and red tiles everywhere else. In all cases, both blue and red tiles must be used. and the two diagonals must have a common blue tile at the center of the floor. If 81 blue tiles will be used, how many red tiles will be needed?

Find the values of n, if the points (n + 1, 2n), (3n, 2n + 3) and (5n + 1,5n) are collinear. Find the value of k that the four points (4,1,2), (5, k, 6), (5,1,-1) and (7,4,0) are coplanar. Find the value of r if the area of the triangle is formed by the points (-3,6),(4,4) and (r,-2) is 12 sq units. Find the volume of tetrahedron whose vertices are A(1,1,0), B(-4,3,6), C(-1,0,3) and D(2,4,-5).

Chapter 11 Solutions

MATHEMATICS A PRACTICAL ODYSSEY W/ACCESS

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 equilibrium matrix L by solving L T = L for L .

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

Videos

(a)

To find:

The equilibrium matrix L by solving LT=L for L.

(b)

To verify:

The solution LT=L.

Want to see the full answer?

Chapter 11 Solutions

(a) To find: The equilibrium matrix L by solving L T = L for L .

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

Videos

(a) To find: The equilibrium matrix L by solving LT=L for L.

(b) To verify: The solution LT=L.

Want to see the full answer?

Chapter 11 Solutions

(a)

To find:

The equilibrium matrix L by solving LT=L for L.

(b)

To verify:

The solution LT=L.