/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q24E 24: Find all eigenvalues of the ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 7: Q24E (page 336)

24: Find all eigenvalues of the positive transition matrix

A=[0.50.250.50.75]

See Definitions 2.1.4 and 2.3.10.

Short Answer

Expert verified

All eigenvalues of the positive transition matrix:

位1=0.25,almu(0.25)=1位2=1,almu(1)=1

Step by step solution

01

Step 1:Transition Matrix

Transition matrix may refer to: The matrix associated with a change of basis for a vector space. Stochastic matrix, a square matrix used to describe the transitions of a Markov chain. State-transition matrix, a matrix whose product with the state vector. at an initial time.

02

Sketching a phase portrait of the dynamical system

As we clearly now that,

det(A-位l)=00.5-位0.250.50.75-位=00.5-位0.75-位-0.125=0位2-1.25位+0.25=0位-0.25位-1=0位1=0.25,位2=1

Hence, the final answer is:

位1=0.25,almu(0.25)=1位2=1,almu(1)=1

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

Most popular questions from this chapter

For each of the matrices in Exercises 1 through 13, find all real eigenvalues, with their algebraic multiplicities. Show your work. Do not use technology.

[010001100]

Consider the matrix A=|abba|where aand bare arbitrary constants. Find all eigenvalues of A.

Question: If a vectorv鈫�is an eigenvector of both AandB, isv鈫� necessarily an eigenvector ofAB?

If v鈬赌 is an eigenvector of matrix A with associated eigenvalue 3 , show that v鈬赌is an image of matrix A .

Is v鈬赌an eigenvector of 7 A? If so, what is the eigenvalue?
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Decision Maths

Read Explanation

Probability and Statistics

Read Explanation

Calculus

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Pure Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.