
Finite Mathematics & Its Applications (12th Edition)
12th Edition
ISBN: 9780134507125
Author: Goldstein
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Question
Chapter 8, Problem 2RE
To determine
Whether the matrix
Expert Solution & Answer

Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
1.
2.
Define f: ZZ and 9: ZZ by f(x)=3x+1 and g(x) = x².
(a) Calculate (go f)(2).
(b) Find an explicit formula for the function gof.
Define f: R2 R2 by f(x, y) = (3x+y, 5x+2y). Give an explicit formula for f-1.
Verify that it is the inverse of f. Do not include a derivation for f¹ unless it is for the verification.
Suppose that two toothpaste companies compete for customers in a fixed market in which each
customer uses either Brand A or Brand B. Suppose also that a market analysis shows that the
buying habits of the customers fit the following pattern in the quarters that were analyzed:
each quarter (three-month period), 30% of A users will switch to B, while the rest stay with
A. Moreover, 40% of B users will switch to A in a given quarter, while the remaining B users
will stay with B. Finally assume that this pattern does not vary from quarter to quarter.
(a) If A initially has all of the customers, what are the market shares 2 quarters later?
(b) If A initially has all of the customers, what are the market shares 20 quarters later?
(c) If B initially has all of the customers, what are the market shares 2 quarters later?
(d) If B initially has all of the customers, what are the market shares 20 quarters later?
1. The regular representation of a finite group G is a pair (Vreg, Dreg). Vreg is a vector space
and Dreg is a homomorphism.
(a) What is the dimension of Vreg?
(b) Describe a basis for Vreg and give a formula for Dreg. Hence explain why the homo-
morphism property is satisfied by Dreg.
(c) Prove that the character ✗reg (g) defined by tr Dreg (g) is zero if g is not the identity
element of the group.
(d) A finite group of order 60 has five irreducible representations R1, R2, R3, R4, R5. R₁
is the trivial representation. R2, R3, R4 have dimensions (3,3,4) respectively. What is the
dimension of R5? Explain how your solution is related to the decomposition of the regular
representation as a direct sum of irreducible representations (You can assume without proof
the properties of this decomposition which have been explained in class and in the lecture
notes).
(e) A
group element
has characters in the irreducible representations R2, R3, R4 given
as
R3
R2 (g)
= -1
X³ (g) = −1 ; XR4 (g) = 0…
Chapter 8 Solutions
Finite Mathematics & Its Applications (12th Edition)
Ch. 8.1 - 1. Is a stochastic matrix?
Ch. 8.1 - 2. Learning Process An elementary learning process...Ch. 8.1 - In Exercises 1-6, determine whether or not the...Ch. 8.1 - In Exercises 1-6, determine whether or not the...Ch. 8.1 - In Exercises 1-6, determine whether or not the...Ch. 8.1 - Prob. 4ECh. 8.1 - In Exercises 1-6, determine whether or not the...Ch. 8.1 - Prob. 6ECh. 8.1 - In Exercises 7–12, write a stochastic matrix...Ch. 8.1 - Prob. 8E
Ch. 8.1 - Prob. 9ECh. 8.1 - Prob. 10ECh. 8.1 - Prob. 11ECh. 8.1 - Prob. 12ECh. 8.1 - In Exercises 13–18, draw a transition diagram...Ch. 8.1 - Prob. 14ECh. 8.1 - Prob. 15ECh. 8.1 - Prob. 16ECh. 8.1 - Prob. 17ECh. 8.1 - Prob. 18ECh. 8.1 - Woman in the Labor Force Referring to Example 5,...Ch. 8.1 - Prob. 20ECh. 8.1 - Cell Phone Usag e A cell phone provider classifies...Ch. 8.1 - Health Plan Option A university faculty health...Ch. 8.1 - Population Movement The Southwestern states were...Ch. 8.1 - Prob. 24ECh. 8.1 - T-Maze Each day, mice are put into a T-maze (a...Ch. 8.1 - 26. Analysis of a Poem In 1913, Markov analyzed a...Ch. 8.1 - Taxi Zones Refer to Example 7 (taxi zones). If,...Ch. 8.1 - Fitness A group of physical fitness devotees works...Ch. 8.1 - 29. Political Views According to the Higher...Ch. 8.1 - 30. Student Residences According to the Higher...Ch. 8.1 - Prob. 31ECh. 8.1 - Prob. 32ECh. 8.1 - Prob. 33ECh. 8.1 - Prob. 34ECh. 8.1 - Ehrenfest Urn Model The Ehrenfest urn model was...Ch. 8.1 - Prob. 36ECh. 8.1 - Prob. 37ECh. 8.1 - Prob. 38ECh. 8.1 - Prob. 39ECh. 8.1 - Prob. 40ECh. 8.1 - Prob. 41ECh. 8.1 - Prob. 42ECh. 8.1 - Prob. 43ECh. 8.1 - Prob. 44ECh. 8.1 - Prob. 45ECh. 8.1 - Prob. 46ECh. 8.1 - Prob. 47ECh. 8.1 - Prob. 48ECh. 8.1 - Prob. 49ECh. 8.1 - Repeat Exercise 49 for the matrices of Exercise...Ch. 8.1 - Prob. 51ECh. 8.1 - Prob. 52ECh. 8.2 - Solutions can be found following the section...Ch. 8.2 - Solutions can be found following the section...Ch. 8.2 - Solutions can be found following the section...Ch. 8.2 - In Exercises 16, determine whether or not the...Ch. 8.2 - In Exercises 16, determine whether or not the...Ch. 8.2 - In Exercises 16, determine whether or not the...Ch. 8.2 - In Exercises 16, determine whether or not the...Ch. 8.2 - In Exercises 1–6, determine whether or not the...Ch. 8.2 - In Exercises 16, determine whether or not the...Ch. 8.2 - In Exercises 7–12, find the stable distribution...Ch. 8.2 - In Exercises 712, find the stable distribution for...Ch. 8.2 - In Exercises 712, find the stable distribution for...Ch. 8.2 - In Exercises 7–12, find the stable distribution...Ch. 8.2 - In Exercises 712, find the stable distribution for...Ch. 8.2 - In Exercises 712, find the stable distribution for...Ch. 8.2 - Prob. 13ECh. 8.2 - Voter Patterns Refer to Exercise 24 of Section...Ch. 8.2 - Prob. 15ECh. 8.2 - Computer Reliability A certain university has a...Ch. 8.2 - Brand Loyalty Suppose that 60% of people who own a...Ch. 8.2 - 18. Transportation Modes Commuters can get into...Ch. 8.2 - Weather Patterns The changes in weather from day...Ch. 8.2 - 20. Women in the Labor Force Refer to the...Ch. 8.2 - 21. Car Rentals The Day-by-Day car rental agency...Ch. 8.2 - 22. Fitness Refer to Exercise 28 of Section 8.1....Ch. 8.2 - Genetics With respect to a certain gene,...Ch. 8.2 - 24. Weather Patterns The day-to-day changes in...Ch. 8.2 - Prob. 25ECh. 8.2 - Prob. 26ECh. 8.2 - Birth Weights Refer to Exercise 33 of Section 8.1....Ch. 8.2 - Bird Migrations Figure 5 describes the migration...Ch. 8.2 - Prob. 29ECh. 8.2 - Prob. 30ECh. 8.2 - Prob. 31ECh. 8.2 - Prob. 32ECh. 8.3 - 1. When an absorbing stochastic matrix is...Ch. 8.3 - Prob. 2CYUCh. 8.3 - Is [1.400.2.10.4.9] an absorbing stochastic...Ch. 8.3 - In Exercises 14, determine whether the transition...Ch. 8.3 - In Exercises 14, determine whether the transition...Ch. 8.3 - In Exercises 1–4, determine whether the transition...Ch. 8.3 - Prob. 4ECh. 8.3 - Prob. 5ECh. 8.3 - In Exercises 58, determine whether the given...Ch. 8.3 - Prob. 7ECh. 8.3 - Prob. 8ECh. 8.3 - Prob. 9ECh. 8.3 - Prob. 10ECh. 8.3 - Prob. 11ECh. 8.3 - In Exercises 912, convert the absorbing stochastic...Ch. 8.3 - The matrices in Exercises 1318 are absorbing...Ch. 8.3 - Prob. 14ECh. 8.3 - Prob. 15ECh. 8.3 - The matrices in Exercises 1318 are absorbing...Ch. 8.3 - Prob. 17ECh. 8.3 - Prob. 18ECh. 8.3 - Prob. 19ECh. 8.3 - Gambler’s Ruin Exercises 19 and 20 refer to...Ch. 8.3 - Gambler’s Ruin Exercises 19 and 20 refer to...Ch. 8.3 - Prob. 22ECh. 8.3 - Mouse in a Maze A mouse is placed in one of the...Ch. 8.3 - Prob. 24ECh. 8.3 - 25. Class Standings Suppose that the ...Ch. 8.3 - Quality Control A manufacturer of precise...Ch. 8.3 - Prob. 27ECh. 8.3 - Job Mobility The managers in a company are...Ch. 8.3 - Prob. 29ECh. 8.3 - Prob. 30ECh. 8.3 - Collecting Quotations A soft drink manufacturer...Ch. 8.3 - Tennis Consider a game of tennis between player A...Ch. 8.3 - Prob. 33ECh. 8.3 - Repeat Exercise 33 for the matrix...Ch. 8 - 1. What is a Markov process?
Ch. 8 - Prob. 2FCCECh. 8 - Prob. 3FCCECh. 8 - Prob. 4FCCECh. 8 - Define regular stochastic matrix.Ch. 8 - 6. Define the stable matrix and the stable...Ch. 8 - Prob. 7FCCECh. 8 - Prob. 8FCCECh. 8 - Prob. 9FCCECh. 8 - Prob. 10FCCECh. 8 - Prob. 11FCCECh. 8 - In Exercises 16, determine whether or not the...Ch. 8 - Prob. 2RECh. 8 - Prob. 3RECh. 8 - Prob. 4RECh. 8 - Prob. 5RECh. 8 - In Exercises 16, determine whether or not the...Ch. 8 - Prob. 7RECh. 8 - Prob. 8RECh. 8 - Prob. 9RECh. 8 - Quality Control In a certain factory, some...Ch. 8 - Prob. 11RECh. 8 - 12. Mouse in a House Figure 1 gives the layout of...Ch. 8 - 13. Which of the following is the stable...Ch. 8 - Prob. 14RECh. 8 - Prob. 15RECh. 8 - Prob. 16RECh. 8 - Prob. 17RECh. 8 - Prob. 18RECh. 8 - Prob. 19RECh. 8 - Prob. 20RECh. 8 - Prob. 21RECh. 8 - Prob. 22RECh. 8 - Prob. 1PCh. 8 - Prob. 2PCh. 8 - Prob. 3PCh. 8 - We will now show that the product of any two ...Ch. 8 - Prob. 5PCh. 8 - We will now show that the product of any two ...Ch. 8 - Prob. 7P
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.Similar questions
- 3.12 (B). A horizontal beam AB is 4 m long and of constant flexural rigidity. It is rigidly built-in at the left-hand end A and simply supported on a non-yielding support at the right-hand end B. The beam carries Uniformly distributed vertical loading of 18 kN/m over its whole length, together with a vertical downward load of 10KN at 2.5 m from the end A. Sketch the S.F. and B.M. diagrams for the beam, indicating all main values. Cl. Struct. E.] CS.F. 45,10,376 KN, B.M. 186, +36.15 kNm.7arrow_forwardDraw the isoclines with their direction markers and sketch several solution curves, including the curve satisfying the given initial conditions. 1) y'=x + 2y ; y(0) = 1 and 2) y' = x², y(0)=1arrow_forwardQize f(x) = x + 2x2 - 2 x² + 4x²² - Solve the equation using Newton Raphsonarrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage

Linear Algebra: A Modern Introduction
Algebra
ISBN:9781285463247
Author:David Poole
Publisher:Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage
Finite Math: Markov Chain Example - The Gambler's Ruin; Author: Brandon Foltz;https://www.youtube.com/watch?v=afIhgiHVnj0;License: Standard YouTube License, CC-BY
Introduction: MARKOV PROCESS And MARKOV CHAINS // Short Lecture // Linear Algebra; Author: AfterMath;https://www.youtube.com/watch?v=qK-PUTuUSpw;License: Standard Youtube License
Stochastic process and Markov Chain Model | Transition Probability Matrix (TPM); Author: Dr. Harish Garg;https://www.youtube.com/watch?v=sb4jo4P4ZLI;License: Standard YouTube License, CC-BY