Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN: 9781305658004
Author: Ron Larson
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Videos
Question
Chapter 7.CR, Problem 49CR
To determine
To find:
The steady state probability
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Find the steady-state vector for the matrix below.
0.6 0.2 0.2
P = 0.2 0.6 0.2
0.2 0.2 0.6
q=
-(Type an integer or simplified fraction for each matrix element.)
(Absorbing Markov Chain) An insurance company wants to make sure they have sufficient
resources to cover patient services for a particular illness. The insurance company makes three
health condition categories for patients with this illness: Died (1), Poor (2), Good (3). The
insurance company has learned that the transition matrix for a one week cycle is:
123
1
2
3
1
0
0
0.08
0.8 0.12
0.02 0.02 0.96]
estin
Stationary Matrix
Consider an example where a company initially has a 10% market share. Using an
advertising campaign, the probability of a customer will use and stick to the company
brand is 80%. On the other hand, the probability of a customers that uses the other
Brand is 40%.
• Question: If the probabilities remain valid over a long period of time, What
happens to the companies market share?
Chapter 7 Solutions
Elementary Linear Algebra (MindTap Course List)
Ch. 7.1 - Verifying Eigenvalues and Eigenvectors in...Ch. 7.1 - Verifying Eigenvalues and EigenvectorsIn Exercises...Ch. 7.1 - Verifying Eigenvalues and EigenvectorsIn Exercises...Ch. 7.1 - Verifying Eigenvalues and Eigenvectors in...Ch. 7.1 - Verifying Eigenvalues and EigenvectorsIn Exercises...Ch. 7.1 - Verifying Eigenvalues and EigenvectorsIn Exercises...Ch. 7.1 - Prob. 7ECh. 7.1 - Prob. 8ECh. 7.1 - Determining Eigenvectors In Exercise 9-12,...Ch. 7.1 - Determining Eigenvectors In Exercise 9-12,...
Ch. 7.1 - Determining Eigenvectors In Exercise 9-12,...Ch. 7.1 - Prob. 12ECh. 7.1 - Prob. 13ECh. 7.1 - Prob. 14ECh. 7.1 - Characteristic Equation, Eigenvalues, and...Ch. 7.1 - Characteristic Equation, Eigenvalues, and...Ch. 7.1 - Characteristic Equation, Eigenvalues, and...Ch. 7.1 - Prob. 18ECh. 7.1 - Characteristic Equation, Eigenvalues, and...Ch. 7.1 - Prob. 20ECh. 7.1 - Characteristic Equation, Eigenvalues and...Ch. 7.1 - Characteristic Equation, Eigenvalues and...Ch. 7.1 - Characteristic Equation, Eigenvalues and...Ch. 7.1 - Prob. 24ECh. 7.1 - Characteristic Equation, Eigenvalues and...Ch. 7.1 - Characteristic Equation, Eigenvalues and...Ch. 7.1 - Characteristic Equation, Eigenvalues and...Ch. 7.1 - Characteristic Equation, Eigenvalues and...Ch. 7.1 - Prob. 29ECh. 7.1 - Prob. 30ECh. 7.1 - Prob. 31ECh. 7.1 - Prob. 32ECh. 7.1 - Prob. 33ECh. 7.1 - Prob. 34ECh. 7.1 - Prob. 35ECh. 7.1 - Prob. 36ECh. 7.1 - Prob. 37ECh. 7.1 - Prob. 38ECh. 7.1 - Prob. 39ECh. 7.1 - Finding EigenvaluesIn Exercises 29-40, use a...Ch. 7.1 - Eigenvalues of Triangular and Diagonal Matrices In...Ch. 7.1 - Eigenvalues of Triangular and Diagonal Matrices In...Ch. 7.1 - Prob. 43ECh. 7.1 - Eigenvalues of Triangular and Diagonal Matrices In...Ch. 7.1 - Eigenvalues and Eigenvectors of Linear...Ch. 7.1 - Prob. 46ECh. 7.1 - Eigenvalues and Eigenvectors of Linear...Ch. 7.1 - Eigenvalues and Eigenvectors of Linear...Ch. 7.1 - Cayley-Hamilton TheoremIn Exercises 49-52,...Ch. 7.1 - Cayley-Hamilton TheoremIn Exercises 49-52,...Ch. 7.1 - Prob. 51ECh. 7.1 - Prob. 52ECh. 7.1 - Prob. 53ECh. 7.1 - Prob. 54ECh. 7.1 - Prob. 55ECh. 7.1 - Prob. 56ECh. 7.1 - Prob. 57ECh. 7.1 - Proof Prove that A and AT have the same...Ch. 7.1 - Prob. 59ECh. 7.1 - Define T:R2R2 by T(v)=projuv Where u is a fixed...Ch. 7.1 - Prob. 61ECh. 7.1 - Prob. 62ECh. 7.1 - Prob. 63ECh. 7.1 - Prob. 64ECh. 7.1 - Prob. 65ECh. 7.1 - Show that A=[0110] has no real eigenvalues.Ch. 7.1 - True or False? In Exercises 67 and 68, determine...Ch. 7.1 - True or False? In Exercises 67 and 68, determine...Ch. 7.1 - Finding the Dimension of an Eigenspace In...Ch. 7.1 - Finding the Dimension of an Eigenspace In...Ch. 7.1 - Prob. 71ECh. 7.1 - Prob. 72ECh. 7.1 - Prob. 73ECh. 7.1 - Prob. 74ECh. 7.1 - Prob. 75ECh. 7.1 - Define T:P2P2 by...Ch. 7.1 - Prob. 77ECh. 7.1 - Find all values of the angle for which the matrix...Ch. 7.1 - Prob. 79ECh. 7.1 - Prob. 80ECh. 7.1 - Prob. 81ECh. 7.2 - Diagonalizable Matrices and Eigenvalues In...Ch. 7.2 - Diagonalizable Matrices and Eigenvalues In...Ch. 7.2 - Diagonalizable Matrices and Eigenvalues In...Ch. 7.2 - Diagonalizable Matrices and Eigenvalues In...Ch. 7.2 - Diagonalizable Matrices and Eigenvalues In...Ch. 7.2 - Prob. 6ECh. 7.2 - Diagonalizing a Matrix In Exercise 7-14, find if...Ch. 7.2 - Prob. 8ECh. 7.2 - Diagonalizing a Matrix In Exercise 7-14, find if...Ch. 7.2 - Diagonalizing a Matrix In Exercise 7-14, find if...Ch. 7.2 - Diagonalizing a Matrix In Exercise 7-14, find if...Ch. 7.2 - Diagonalizing a Matrix In Exercise 7-14, find if...Ch. 7.2 - Diagonalizing a Matrix In Exercise 7-14, find if...Ch. 7.2 - Prob. 14ECh. 7.2 - Show That a Matrix Is Not Diagonalizable In...Ch. 7.2 - Prob. 16ECh. 7.2 - Show That a Matrix Is Not Diagonalizable In...Ch. 7.2 - Show That a Matrix Is Not Diagonalizable In...Ch. 7.2 - Show That a Matrix Is Not Diagonalizable In...Ch. 7.2 - Show That a Matrix Is Not Diagonalizable In...Ch. 7.2 - Prob. 21ECh. 7.2 - Prob. 22ECh. 7.2 - Determine a Sufficient Condition for...Ch. 7.2 - Determine a Sufficient Condition for...Ch. 7.2 - Determine a Sufficient Condition for...Ch. 7.2 - Determine a Sufficient Condition for...Ch. 7.2 - Finding a Basis In Exercises 27-30, find a basis B...Ch. 7.2 - Finding a Basis In Exercises 27-30, find a basis B...Ch. 7.2 - Prob. 29ECh. 7.2 - Prob. 30ECh. 7.2 - Prob. 31ECh. 7.2 - Prob. 32ECh. 7.2 - Prob. 33ECh. 7.2 - Finding a Power of a Matrix In Exercises 33-36,...Ch. 7.2 - Prob. 35ECh. 7.2 - Prob. 36ECh. 7.2 - True or False? In Exercises 37 and 38, determine...Ch. 7.2 - True or False? In Exercises 37 and 38, determine...Ch. 7.2 - Are the two matrices similar? If so, find a matrix...Ch. 7.2 - Prob. 40ECh. 7.2 - Prob. 41ECh. 7.2 - Proof Prove that if matrix A is diagonalizable,...Ch. 7.2 - Proof Prove that if matrix A is diagonalizable...Ch. 7.2 - Prob. 44ECh. 7.2 - Prob. 45ECh. 7.2 - Guide Proof Prove nonzero nilpotent matrices are...Ch. 7.2 - Prob. 47ECh. 7.2 - CAPSTONE Explain how to determine whether an nn...Ch. 7.2 - Prob. 49ECh. 7.2 - Showing That a Matrix Is Not Diagonalizable In...Ch. 7.3 - Determining Whether a Matrix Is Symmetric In...Ch. 7.3 - Prob. 2ECh. 7.3 - Proof In Exercise 3-6, prove that the symmetric...Ch. 7.3 - Prob. 4ECh. 7.3 - Prob. 5ECh. 7.3 - Prob. 6ECh. 7.3 - Finding Eigenvalues and Dimensions of Eigen spaces...Ch. 7.3 - Finding Eigenvalues and Dimensions of Eigen spaces...Ch. 7.3 - Finding Eigenvalues and Dimensions of Eigen spaces...Ch. 7.3 - Finding Eigenvalues and Dimensions of Eigen spaces...Ch. 7.3 - Finding Eigenvalues and Dimensions of Eigen spaces...Ch. 7.3 - Finding Eigenvalues and Dimensions of Eigen spaces...Ch. 7.3 - Finding Eigenvalues and Dimensions of Eigen spaces...Ch. 7.3 - Prob. 14ECh. 7.3 - Prob. 15ECh. 7.3 - Prob. 16ECh. 7.3 - Prob. 17ECh. 7.3 - Prob. 18ECh. 7.3 - Determine Whether a Matrix Is Orthogonal In...Ch. 7.3 - Prob. 20ECh. 7.3 - Prob. 21ECh. 7.3 - Prob. 22ECh. 7.3 - Prob. 23ECh. 7.3 - Prob. 24ECh. 7.3 - Prob. 25ECh. 7.3 - Prob. 26ECh. 7.3 - Prob. 27ECh. 7.3 - Prob. 28ECh. 7.3 - Prob. 29ECh. 7.3 - Prob. 30ECh. 7.3 - Prob. 31ECh. 7.3 - Prob. 32ECh. 7.3 - Prob. 33ECh. 7.3 - Prob. 34ECh. 7.3 - Prob. 35ECh. 7.3 - Eigenvectors of Symmetric Matrix In Exercises...Ch. 7.3 - Prob. 37ECh. 7.3 - Prob. 38ECh. 7.3 - Prob. 39ECh. 7.3 - Orthogonally Diagonalizable Matrices In Exercise...Ch. 7.3 - Prob. 41ECh. 7.3 - Prob. 42ECh. 7.3 - Prob. 43ECh. 7.3 - Prob. 44ECh. 7.3 - Orthogonal Diagonalization In Exercise 43-52, find...Ch. 7.3 - Orthogonal Diagonalization In Exercise 43-52, find...Ch. 7.3 - Orthogonal Diagonalization In Exercise 4-52, find...Ch. 7.3 - Prob. 48ECh. 7.3 - Prob. 49ECh. 7.3 - Orthogonal Diagonalization In Exercise 43-52, find...Ch. 7.3 - Orthogonal Diagonalization In Exercise 4-52, find...Ch. 7.3 - Prob. 52ECh. 7.3 - Prob. 53ECh. 7.3 - Prob. 54ECh. 7.3 - Prob. 55ECh. 7.3 - Prob. 56ECh. 7.3 - Prob. 57ECh. 7.3 - Prob. 58ECh. 7.3 - Prob. 59ECh. 7.3 - Find ATA and AAT for the matrix below. What do you...Ch. 7.4 - Finding Age Distribution Vectors In Exercises 1-6,...Ch. 7.4 - Prob. 2ECh. 7.4 - Prob. 3ECh. 7.4 - Finding Age Distribution Vectors In Exercises 1-6,...Ch. 7.4 - Prob. 5ECh. 7.4 - Prob. 6ECh. 7.4 - Population Growth Model A population has the...Ch. 7.4 - Population Growth Model A population has the...Ch. 7.4 - Prob. 9ECh. 7.4 - Find the limit if it exists of Anx1 as n...Ch. 7.4 - Prob. 11ECh. 7.4 - Prob. 12ECh. 7.4 - Prob. 13ECh. 7.4 - Prob. 14ECh. 7.4 - Prob. 15ECh. 7.4 - Prob. 16ECh. 7.4 - Prob. 17ECh. 7.4 - Prob. 18ECh. 7.4 - Prob. 19ECh. 7.4 - Prob. 20ECh. 7.4 - Solving a System of Linear Differential Equations...Ch. 7.4 - Solving a System of Linear Differential Equations...Ch. 7.4 - Prob. 23ECh. 7.4 - Solving a System of Linear Differential Equations...Ch. 7.4 - Prob. 25ECh. 7.4 - Prob. 26ECh. 7.4 - Solving a System of Linear Differential Equations...Ch. 7.4 - Prob. 28ECh. 7.4 - Prob. 29ECh. 7.4 - Prob. 30ECh. 7.4 - Prob. 31ECh. 7.4 - Prob. 32ECh. 7.4 - Prob. 33ECh. 7.4 - Prob. 34ECh. 7.4 - Prob. 35ECh. 7.4 - Prob. 36ECh. 7.4 - Prob. 37ECh. 7.4 - Prob. 38ECh. 7.4 - Prob. 39ECh. 7.4 - Prob. 40ECh. 7.4 - Prob. 41ECh. 7.4 - Prob. 42ECh. 7.4 - Prob. 43ECh. 7.4 - Prob. 44ECh. 7.4 - Prob. 45ECh. 7.4 - Prob. 46ECh. 7.4 - Rotation of a Conic In Exercises 45-52, use the...Ch. 7.4 - Prob. 48ECh. 7.4 - Prob. 49ECh. 7.4 - Prob. 50ECh. 7.4 - Prob. 51ECh. 7.4 - Prob. 52ECh. 7.4 - Prob. 53ECh. 7.4 - Prob. 54ECh. 7.4 - Prob. 55ECh. 7.4 - Prob. 56ECh. 7.4 - Prob. 57ECh. 7.4 - Prob. 58ECh. 7.4 - Prob. 59ECh. 7.4 - Prob. 60ECh. 7.4 - Prob. 61ECh. 7.4 - Prob. 62ECh. 7.4 - Prob. 63ECh. 7.4 - Prob. 64ECh. 7.4 - Prob. 65ECh. 7.4 - Prob. 66ECh. 7.4 - Prob. 67ECh. 7.4 - Use your schools library, the Internet, or some...Ch. 7.CR - Characteristic Equation, Eigenvalues, and Basis In...Ch. 7.CR - Characteristic Equation, Eigenvalues, and Basis In...Ch. 7.CR - Characteristic Equation, Eigenvalues, and Basis In...Ch. 7.CR - Prob. 4CRCh. 7.CR - Characteristic Equation, Eigenvalues, and Basis In...Ch. 7.CR - Prob. 6CRCh. 7.CR - Characteristics Equation, Eigenvalues, and Basis...Ch. 7.CR - Characteristics Equation, Eigenvalues, and Basis...Ch. 7.CR - Determining Whether a Matrix Is DiagonalizableIn...Ch. 7.CR - Prob. 10CRCh. 7.CR - Determining Whether a Matrix Is DiagonalizableIn...Ch. 7.CR - Prob. 12CRCh. 7.CR - Determining Whether a Matrix Is DiagonalizableIn...Ch. 7.CR - Prob. 14CRCh. 7.CR - For what values of a does the matrix A=[01a1] have...Ch. 7.CR - Prob. 16CRCh. 7.CR - Writing In Exercises 17-20, explain why the given...Ch. 7.CR - Prob. 18CRCh. 7.CR - Writing In Exercises 17-20, explain why the given...Ch. 7.CR - Prob. 20CRCh. 7.CR - Determine Whether Two Matrices Are Similar In...Ch. 7.CR - Determine Whether Two Matrices Are Similar In...Ch. 7.CR - Determine Whether Two Matrices Are Similar In...Ch. 7.CR - Determine Whether Two Matrices Are Similar In...Ch. 7.CR - Determining Symmetric and Orthogonal Matrices In...Ch. 7.CR - Prob. 26CRCh. 7.CR - Determining Symmetric and Orthogonal Matrices In...Ch. 7.CR - Prob. 28CRCh. 7.CR - Prob. 29CRCh. 7.CR - Determine Symmetric and Orthogonal Matrices In...Ch. 7.CR - Prob. 31CRCh. 7.CR - Prob. 32CRCh. 7.CR - Prob. 33CRCh. 7.CR - Prob. 34CRCh. 7.CR - Prob. 35CRCh. 7.CR - Prob. 36CRCh. 7.CR - Orthogonally Diagonalizable Matrices In Exercises...Ch. 7.CR - Prob. 38CRCh. 7.CR - Orthogonally Diagonalizable Matrices In Exercises...Ch. 7.CR - Prob. 40CRCh. 7.CR - Prob. 41CRCh. 7.CR - Prob. 42CRCh. 7.CR - Prob. 43CRCh. 7.CR - Prob. 44CRCh. 7.CR - Prob. 45CRCh. 7.CR - Orthogonal Diagonalization In Exercises 41-46,...Ch. 7.CR - Prob. 47CRCh. 7.CR - Prob. 48CRCh. 7.CR - Prob. 49CRCh. 7.CR - Prob. 50CRCh. 7.CR - Prob. 51CRCh. 7.CR - Prob. 52CRCh. 7.CR - Steady State Probability Vector In Exercises...Ch. 7.CR - Prob. 54CRCh. 7.CR - Prob. 55CRCh. 7.CR - Prob. 56CRCh. 7.CR - Prob. 57CRCh. 7.CR - Prob. 58CRCh. 7.CR - Prob. 59CRCh. 7.CR - Prob. 60CRCh. 7.CR - Prob. 61CRCh. 7.CR - Prob. 62CRCh. 7.CR - Prob. 63CRCh. 7.CR - a Find a symmetric matrix B such that B2=A for...Ch. 7.CR - Determine all nn symmetric matrices that have 0 as...Ch. 7.CR - Prob. 66CRCh. 7.CR - Prob. 67CRCh. 7.CR - Prob. 68CRCh. 7.CR - Prob. 69CRCh. 7.CR - True or False? In Exercises 69 and 70, determine...Ch. 7.CR - Prob. 71CRCh. 7.CR - Prob. 72CRCh. 7.CR - Prob. 73CRCh. 7.CR - Prob. 74CRCh. 7.CR - Prob. 75CRCh. 7.CR - Prob. 76CRCh. 7.CR - Prob. 77CRCh. 7.CR - Prob. 78CRCh. 7.CR - Prob. 79CRCh. 7.CR - Prob. 80CRCh. 7.CR - Prob. 81CRCh. 7.CR - Prob. 82CRCh. 7.CR - Prob. 83CRCh. 7.CR - Prob. 84CRCh. 7.CR - Prob. 85CRCh. 7.CR - Prob. 86CRCh. 7.CR - Prob. 87CRCh. 7.CR - Prob. 88CRCh. 7.CM - Prob. 1CMCh. 7.CM - In Exercises 1 and 2, determine whether the...Ch. 7.CM - Let T:RnRm be the linear transformation defined by...Ch. 7.CM - Prob. 4CMCh. 7.CM - Find the kernel of the linear transformation...Ch. 7.CM - Let T:R4R2 be the linear transformation defined by...Ch. 7.CM - In Exercises 7-10, find the standard matrix for...Ch. 7.CM - Prob. 8CMCh. 7.CM - Prob. 9CMCh. 7.CM - Prob. 10CMCh. 7.CM - Prob. 11CMCh. 7.CM - Prob. 12CMCh. 7.CM - Prob. 13CMCh. 7.CM - Prob. 14CMCh. 7.CM - Prob. 15CMCh. 7.CM - Prob. 16CMCh. 7.CM - Prob. 17CMCh. 7.CM - Prob. 18CMCh. 7.CM - In Exercises 19-22, find the eigenvalues and the...Ch. 7.CM - Prob. 20CMCh. 7.CM - Prob. 21CMCh. 7.CM - Prob. 22CMCh. 7.CM - In Exercises 23 and 24, find a nonsingular matrix...Ch. 7.CM - In Exercises 23 and 24, find a nonsingular matrix...Ch. 7.CM - Find a basis B for R3 such that the matrix for the...Ch. 7.CM - Find an orthogonal matrix P such that PTAP...Ch. 7.CM - Use the Gram-Schmidt orthonormalization process to...Ch. 7.CM - Prob. 28CMCh. 7.CM - Prob. 29CMCh. 7.CM - Prob. 30CMCh. 7.CM - Prob. 31CMCh. 7.CM - Prove that if A is similar to B and A is...
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.Similar questions
- Stochastic Matrices In Exercise 1-6, determine whether the matrix is stochastic. [0.30.50.20.10.20.70.80.10.1]arrow_forwardProof Prove that when P is a regular stochastic matrix, the corresponding regular Markov chain PX0,P2X0,P3X0,... approaches a unique steady state matrix X.arrow_forwardTrue or False? In Exercises 55and 56, determine whether each statement is true or false. If a statement is true, give a reason or cite an appropriate statement from the text. If a statement is false, provide an example that shows that the statement is not true in all cases or cite an appropriate statement from the text. a If P is the transition matrix from a basis B to B, then P1 is the transition matrix from B to B. b To perform the change of basis from a nonstandard basis B to the standard basis B, the transition matrix P1 is simply B. c The coordinate matrix of p=3+x+5x2 relative to the standard basis for P2 is [p]S=[513]T.arrow_forward
- show all work) In a certain town, it haeen observed that · if a day is sunny, then 4 out of 5 times it is followed by a sunny day, · if a day is cloudy, then it has 70% chance of being followed by another cloudy one. a. Let St) and c® represent the probability of the ith day being sunny or cloudy, respectively. Find the 2 x 2 matrix A such that [S(i+1)] = A ;(i+1 b. Show that A is a regular matrix. c. Show that Ais a stochastic matrix. d. Starting with a sunny day, calculate the probability vectors for i = 1,2,3. Repeat this calculation starting with a cloudy day instead. e. Find the stable vector of A and compare it to the vectors obtained in part (d).arrow_forwardThe Eigen values of the matrix A = = 1 1 L1 0 1 0 1 0 1. 0,1,2 0,0,1 0,2,-1 O 0,-1,2 O 0,2,2 Oarrow_forwardProof Prove that if A is an nn matrix, then A-AT is skew-symmetric.arrow_forward
arrow_back_ios
arrow_forward_ios
Recommended textbooks for you
Elementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage Learning
Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:9781305658004
Author:Ron Larson
Publisher:Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:9781285463247
Author:David Poole
Publisher:Cengage Learning
Lecture 46: Eigenvalues & Eigenvectors; Author: IIT Kharagpur July 2018;https://www.youtube.com/watch?v=h5urBuE4Xhg;License: Standard YouTube License, CC-BY
What is an Eigenvector?; Author: LeiosOS;https://www.youtube.com/watch?v=ue3yoeZvt8E;License: Standard YouTube License, CC-BY