Basic College Mathematics (6th Edition) (What's New in Developmental Math)
6th Edition
ISBN: 9780134840420
Author: Elayn Martin-Gay
Publisher: PEARSON
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Chapter B, Problem 12E
a.
To determine
The number of miles the car will travel in
b.
To determine
The number of hours the car will take to travel 627 miles.
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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…
it's not algebra 4th grade
Not use ai please
Chapter B Solutions
Basic College Mathematics (6th Edition) (What's New in Developmental Math)
Ch. B - Suppose you make $16 per hour.
Calculate your...Ch. B - A lab technician needs a solution containing 20...Ch. B - Prob. 3ECh. B - Prob. 4ECh. B - Prob. 5ECh. B - Prob. 6ECh. B - Prob. 7ECh. B - Prob. 8ECh. B - Prob. 9ECh. B - Prob. 10E
Ch. B - Prob. 11ECh. B - A car travels at a rate of 57 miles per hour.
How...Ch. B - A tortilla-making machine makes 16 tortillas per...Ch. B - During a flood watch in New Orleans, Louisiana, an...Ch. B - Prob. 15ECh. B - Prob. 16ECh. B - Prob. 17ECh. B - Prob. 18ECh. B - Prob. 1PFECh. B - Prob. 2PFECh. B - Prob. 3PFECh. B - Prob. 4PFECh. B - Prob. 5PFECh. B - Note: Exercises 1–41 review operations with...Ch. B - Note: Exercises 1–41 review operations with...Ch. B - Note: Exercises 1–41 review operations with...Ch. B - Prob. 9PFECh. B - Prob. 10PFECh. B - Prob. 11PFECh. B - Prob. 12PFECh. B - Prob. 13PFECh. B - Prob. 14PFECh. B - Prob. 15PFECh. B - Prob. 16PFECh. B - Prob. 17PFECh. B - Prob. 18PFECh. B - Note: Exercises 1–41 review operations with...Ch. B - Note: Exercises 1–41 review operations with...Ch. B - Note: Exercises 1–41 review operations with...Ch. B - Prob. 22PFECh. B - Prob. 23PFECh. B - Prob. 24PFECh. B - Prob. 25PFECh. B - Prob. 26PFECh. B - Prob. 27PFECh. B - Prob. 28PFECh. B - Prob. 29PFECh. B - Prob. 30PFECh. B - Prob. 31PFECh. B - Note: Exercises 1–41 review operations with...Ch. B - Note: Exercises 1–41 review operations with...Ch. B - Note: Exercises 1–41 review operations with...Ch. B - Prob. 35PFECh. B - Prob. 36PFECh. B - Prob. 37PFECh. B - Prob. 38PFECh. B - Prob. 39PFECh. B - Prob. 40PFECh. B - Prob. 41PFECh. B - Prob. 42PFECh. B - Prob. 43PFECh. B - Prob. 44PFECh. B - Note: Exercises 42–51 may contain signed numbers....Ch. B - Note: Exercises 42–51 may contain signed numbers....Ch. B - Note: Exercises 42–51 may contain signed numbers....Ch. B - Prob. 48PFECh. B - Prob. 49PFECh. B - Prob. 50PFECh. B - Prob. 51PFE
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