Calculus for Business, Economics, Life Sciences, and Social Sciences (13th Edition)
13th Edition
ISBN: 9780321869838
Author: Raymond A. Barnett, Michael R. Ziegler, Karl E. Byleen
Publisher: PEARSON
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Chapter A.4, Problem 3MP
(A)
To determine
To reduce: The rational expression
(B)
To determine
To reduce: The rational expression
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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 A.4 Solutions
Calculus for Business, Economics, Life Sciences, and Social Sciences (13th Edition)
Ch. A.4 - Reduce each fraction to lowest terms....Ch. A.4 - Reduce each rational expression to lowest terms....Ch. A.4 - Prob. 3MPCh. A.4 - Combine into a single fraction and reduce to...Ch. A.4 - Express as a simple fraction reduced to lowest...Ch. A.4 - In Problems 122, perform the indicated operations...Ch. A.4 - In Problems 122, perform the indicated operations...Ch. A.4 - Prob. 3ECh. A.4 - In Problems 122, perform the indicated operations...Ch. A.4 - Prob. 5E
Ch. A.4 - In Problems 122, perform the indicated operations...Ch. A.4 - Prob. 7ECh. A.4 - Prob. 8ECh. A.4 - In Problems 122, perform the indicated operations...Ch. A.4 - In Problems 122, perform the indicated operations...Ch. A.4 - In Problems 122, perform the indicated operations...Ch. A.4 - In Problems 122, perform the indicated operations...Ch. A.4 - In Problems 122, perform the indicated operations...Ch. A.4 - Prob. 14ECh. A.4 - In Problems 122, perform the indicated operations...Ch. A.4 - In Problems 122, perform the indicated operations...Ch. A.4 - In Problems 122, perform the indicated operations...Ch. A.4 - Prob. 18ECh. A.4 - In Problems 122, perform the indicated operations...Ch. A.4 - In Problems 122, perform the indicated operations...Ch. A.4 - In Problems 122, perform the indicated operations...Ch. A.4 - In Problems 122, perform the indicated operations...Ch. A.4 - In Problems 2334, perform the indicated operations...Ch. A.4 - In Problems 2334, perform the indicated operations...Ch. A.4 - Prob. 25ECh. A.4 - In Problems 2334, perform the indicated operations...Ch. A.4 - In Problems 2334, perform the indicated operations...Ch. A.4 - In Problems 2334, perform the indicated operations...Ch. A.4 - In Problems 2334, perform the indicated operations...Ch. A.4 - Prob. 30ECh. A.4 - Prob. 31ECh. A.4 - In Problems 2334, perform the indicated operations...Ch. A.4 - In Problems 2334, perform the indicated operations...Ch. A.4 - Prob. 34ECh. A.4 - Prob. 35ECh. A.4 - In Problems 3542, imagine that the indicated...Ch. A.4 - Prob. 37ECh. A.4 - In Problems 3542, imagine that the indicated...Ch. A.4 - In Problems 3542, imagine that the indicated...Ch. A.4 - In Problems 3542, imagine that the indicated...Ch. A.4 - In Problems 3542, imagine that the indicated...Ch. A.4 - In Problems 3542, imagine that the indicated...Ch. A.4 - Represent the compound fractions in Problems 4346...Ch. A.4 - Represent the compound fractions in Problems 4346...Ch. A.4 - Represent the compound fractions in Problems 4346...Ch. A.4 - Represent the compound fractions in Problems 4346...
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