Q26E For the matrices A and the vecto... [FREE SOLUTION]

91影视

Linear Algebra With Applications

Otto Bretscher

$Math Studyset 91影视 Explanations$ Math

5th Edition 路 442 pages

ISBN: 9780321796974

Chapter 7: Q26E (page 355)

For the matrices A and the vectors $\overset{鈫�}{x_{0}}$ in Exercises 25 through 29, find $\lim_{t 鈫� 鈭�} (A^{t} {\overset{鈫�}{x}}_{0})$ . Feel free to use Theorem 7.4.1.
$A = [\begin{matrix} 0.4 & 0.5 \\ 0.6 & 0.5 \end{matrix}], \overset{鈫�}{x_{0}} = [\begin{matrix} 0.54 \\ 0.46 \end{matrix}]$

Short Answer

Expert verified

The value of $\lim_{t 鈫� 鈭�} A^{t} \overset{鈫�}{x_{0}} = [\begin{matrix} \frac{5}{11} \\ \frac{6}{11} \end{matrix}]$

Step by step solution

Substituting the given matrix in Ax = x

$A x = x [\begin{matrix} 0.4 & 0.5 \\ 0.6 & 0.5 \end{matrix}] [\begin{matrix} x_{1} \\ x_{2} \end{matrix}] = [\begin{matrix} x_{1} \\ x_{2} \end{matrix}]$

Finding the equilibrium distribution xequ of A

$0.4 x_{1} + 0.5 x_{2} = x_{1}, 0.6 x_{1} + 0.5 x_{2} = x_{2}, x_{1} + x_{2} = 1 x_{1} = \frac{5}{11} x_{2} = \frac{6}{11} x_{e q u} = [\begin{matrix} \frac{5}{11} \\ \frac{6}{11} \end{matrix}] \lim_{t 鈫� 鈭�} A^{t} [\begin{matrix} 0.54 \\ 0.46 \end{matrix}] = [\begin{matrix} \frac{5}{11} \\ \frac{6}{11} \end{matrix}]$

Therefore, the value of $\lim_{t 鈫� 鈭�} A^{t} \overset{鈫�}{x_{0}} = [\begin{matrix} \frac{5}{11} \\ \frac{6}{11} \end{matrix}]$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

Short Answer

Step by step solution

Substituting the given matrix in Ax = x

Finding the equilibrium distribution xequ of A

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Logic and Functions

Applied Mathematics

Mechanics Maths

Probability and Statistics

Pure Maths

Study anywhere. Anytime. Across all devices.

91影视

For the matrices A and the vectorsx0鈫�in Exercises 25 through 29, find limt鈫�鈭�(Atx鈫�0). Feel free to use Theorem 7.4.1.A=[0.40.50.60.5],x0鈫�=[0.540.46]

Short Answer

Step by step solution

Substituting the given matrix in Ax = x

Finding the equilibrium distribution xequ of A

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Logic and Functions

Applied Mathematics

Mechanics Maths

Probability and Statistics

Pure Maths

Study anywhere. Anytime. Across all devices.