Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Students have asked these similar questions
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…
Not use ai please
Find the complete set of values of the
constant c for which the cubic equation
2x³-3x²-12x + c = 0
has three distinct real solutions
Chapter 18 Solutions
Advanced Engineering Mathematics
Ch. 18.1 - Prob. 1PCh. 18.1 - Prob. 2PCh. 18.1 - Prob. 3PCh. 18.1 - Prob. 4PCh. 18.1 - Prob. 5PCh. 18.1 - Prob. 6PCh. 18.1 - Prob. 7PCh. 18.1 - Prob. 9PCh. 18.1 - Prob. 10PCh. 18.1 - Prob. 11P
Ch. 18.1 - Prob. 12PCh. 18.1 - Prob. 13PCh. 18.1 - Prob. 14PCh. 18.1 - Prob. 15PCh. 18.2 - Prob. 1PCh. 18.2 - Prob. 3PCh. 18.2 - Prob. 4PCh. 18.2 - Prob. 6PCh. 18.2 - Prob. 7PCh. 18.2 - Prob. 8PCh. 18.2 - Prob. 9PCh. 18.2 - Prob. 11PCh. 18.2 - Prob. 12PCh. 18.2 - Prob. 13PCh. 18.2 - Prob. 14PCh. 18.2 - Prob. 15PCh. 18.2 - Prob. 16PCh. 18.2 - Prob. 17PCh. 18.2 - Prob. 18PCh. 18.2 - Prob. 19PCh. 18.2 - Prob. 20PCh. 18.3 - Prob. 1PCh. 18.3 - Prob. 2PCh. 18.3 - Prob. 4PCh. 18.3 - Prob. 5PCh. 18.3 - Prob. 6PCh. 18.3 - Prob. 7PCh. 18.3 - Prob. 8PCh. 18.3 - Prob. 9PCh. 18.3 - Prob. 10PCh. 18.3 - Prob. 11PCh. 18.3 - Prob. 12PCh. 18.3 - Prob. 13PCh. 18.3 - Prob. 14PCh. 18.3 - Prob. 15PCh. 18.3 - Prob. 16PCh. 18.3 - Prob. 17PCh. 18.3 - Prob. 18PCh. 18.3 - Prob. 19PCh. 18.3 - Prob. 20PCh. 18.4 - Prob. 1PCh. 18.4 - Prob. 2PCh. 18.4 - Prob. 3PCh. 18.4 - Prob. 4PCh. 18.4 - Prob. 5PCh. 18.4 - Prob. 6PCh. 18.4 - Prob. 7PCh. 18.4 - Prob. 8PCh. 18.4 - Prob. 9PCh. 18.4 - Prob. 10PCh. 18.4 - Prob. 11PCh. 18.4 - Prob. 12PCh. 18.4 - Prob. 13PCh. 18.4 - Prob. 14PCh. 18.4 - Prob. 15PCh. 18.4 - Prob. 16PCh. 18.4 - Prob. 17PCh. 18.4 - Prob. 18PCh. 18.4 - Prob. 19PCh. 18.5 - Prob. 1PCh. 18.5 - Prob. 2PCh. 18.5 - Prob. 3PCh. 18.5 - Prob. 4PCh. 18.5 - Prob. 5PCh. 18.5 - Prob. 6PCh. 18.5 - Prob. 7PCh. 18.5 - Prob. 8PCh. 18.5 - Prob. 9PCh. 18.5 - Prob. 10PCh. 18.5 - Prob. 11PCh. 18.5 - Prob. 12PCh. 18.5 - Prob. 13PCh. 18.5 - Prob. 14PCh. 18.5 - Prob. 15PCh. 18.5 - Prob. 16PCh. 18.5 - Prob. 17PCh. 18.5 - Prob. 18PCh. 18.6 - Prob. 1PCh. 18.6 - Prob. 2PCh. 18.6 - Prob. 3PCh. 18.6 - Prob. 4PCh. 18.6 - Prob. 5PCh. 18.6 - Prob. 6PCh. 18.6 - Prob. 7PCh. 18.6 - Prob. 8PCh. 18.6 - Prob. 9PCh. 18.6 - Prob. 10PCh. 18.6 - Prob. 13PCh. 18.6 - Prob. 14PCh. 18.6 - Prob. 15PCh. 18.6 - Prob. 16PCh. 18.6 - Prob. 17PCh. 18.6 - Prob. 18PCh. 18.6 - Prob. 19PCh. 18.6 - Prob. 20PCh. 18 - Prob. 1RQCh. 18 - Prob. 2RQCh. 18 - Prob. 3RQCh. 18 - Prob. 4RQCh. 18 - Prob. 6RQCh. 18 - Prob. 7RQCh. 18 - Prob. 9RQCh. 18 - Prob. 10RQCh. 18 - Prob. 11RQCh. 18 - Prob. 12RQCh. 18 - Prob. 14RQCh. 18 - Prob. 15RQCh. 18 - Prob. 16RQCh. 18 - Prob. 17RQCh. 18 - Prob. 18RQCh. 18 - Prob. 21RQCh. 18 - Prob. 22RQCh. 18 - Prob. 23RQCh. 18 - Prob. 25RQ
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