/*! 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} Q7.4-21E For the matrices A in Exercise 2... [FREE SOLUTION] | 91Ó°ÊÓ

91Ó°ÊÓ

Log out

Learning Materials

Features

Discover

Chapter 7: Q7.4-21E (page 355)

For the matrices A in Exercise 20 through 24, find limt→∞At. Fell free to use Theorem 7.4.1.

21.A=[0.5    0.250.5    0.75]

Short Answer

Expert verified

limt→∞At=13132323

Step by step solution

01

Definition of matrices

A function is defined as a relationship between a set of inputs that each have one output.

A=0.5    0.250.5    0.75

To find the equilibrium distributionxequ  of  A

Ax=x 0.5    0.250.5     0.75   x1 x2= x1 x2  0.5x1+0.25x2=x1,   0.5x1+0.75x2=x2,   x1+x2=1

x1=13x2=23

02

divide the matrices

⇒ xequ=1323limt→∞At=13132323

Hence,

limt→∞At=13132323

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 91Ó°ÊÓ!

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

If a 2 × 2 matrix A has two distinct eigenvaluesλ1andλ2, show that A is diagonalizable.

Consider the coyotes–roadrunner system discussed in Example 7. Find closed formulas for c(t) and r(t), for the initial populations c0= 100, r0 = 800.

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.

[3-25107002]

In all parts of this problem, let V be the linear space of all 2 × 2 matrices for which [12]is an eigenvector.

(a) Find a basis of V and thus determine the dimension of V.

(b) Consider the linear transformation T (A) = A[12] from V to R2. Find a basis of the image of Tand a basis of the kernel of T. Determine the rank of T .

(c) Consider the linear transformation L(A) = A[13] from V to R2. Find a basis of the image of L and a basis of the kernel of L. Determine the rank of L.

Give an example of a 4×4matrix A without real eigenvalues.
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Logic and Functions

Read Explanation

Mechanics Maths

Read Explanation

Calculus

Read Explanation

Statistics

Read Explanation

Applied Mathematics

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.