Elementary Differential Equations
10th Edition
ISBN: 9780470458327
Author: William E. Boyce, Richard C. DiPrima
Publisher: Wiley, John & Sons, Incorporated
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Chapter 7.1, Problem 18P
To determine
To transform: The given system into system of first order equation.
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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…
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 7 Solutions
Elementary Differential Equations
Ch. 7.1 - In each of Problems 1 through 4, transform the...Ch. 7.1 - Prob. 2PCh. 7.1 - Prob. 3PCh. 7.1 - In each of Problems 1 through 4, transform the...Ch. 7.1 - Prob. 5PCh. 7.1 - In each of Problems 5 and 6, transform the given...Ch. 7.1 - Systems of first order equations can sometimes be...Ch. 7.1 - Prob. 8PCh. 7.1 - Prob. 9PCh. 7.1 - In each of Problems 8 through 12, proceed as in...
Ch. 7.1 - Prob. 11PCh. 7.1 - Prob. 12PCh. 7.1 - Prob. 13PCh. 7.1 - Prob. 14PCh. 7.1 - Prob. 15PCh. 7.1 - Prob. 16PCh. 7.1 - Prob. 17PCh. 7.1 - Prob. 18PCh. 7.1 - Consider the circuit shown in Figure 7.1.2. Let...Ch. 7.1 - Prob. 20PCh. 7.1 - Prob. 21PCh. 7.1 - Prob. 22PCh. 7.1 - Prob. 23PCh. 7.2 - Prob. 1PCh. 7.2 - Prob. 2PCh. 7.2 - Prob. 3PCh. 7.2 - Prob. 4PCh. 7.2 - Prob. 5PCh. 7.2 - Prob. 6PCh. 7.2 - Prob. 7PCh. 7.2 - Prob. 8PCh. 7.2 - Prob. 9PCh. 7.2 - Prob. 10PCh. 7.2 - Prob. 11PCh. 7.2 - Prob. 12PCh. 7.2 - Prob. 13PCh. 7.2 - Prob. 14PCh. 7.2 - Prob. 15PCh. 7.2 - Prob. 16PCh. 7.2 - Prob. 17PCh. 7.2 - Prob. 18PCh. 7.2 - Prob. 19PCh. 7.2 - Prob. 20PCh. 7.2 - Prob. 21PCh. 7.2 - Prob. 22PCh. 7.2 - Prob. 23PCh. 7.2 - Prob. 24PCh. 7.2 - Prob. 25PCh. 7.2 - Prob. 26PCh. 7.3 - In each of Problems 1 through 6, either solve the...Ch. 7.3 - In each of Problems 1 through 6, either solve the...Ch. 7.3 - Prob. 3PCh. 7.3 - Prob. 4PCh. 7.3 - Prob. 5PCh. 7.3 - Prob. 6PCh. 7.3 - Prob. 7PCh. 7.3 - Prob. 8PCh. 7.3 - Prob. 9PCh. 7.3 - Prob. 10PCh. 7.3 - Prob. 11PCh. 7.3 - Prob. 12PCh. 7.3 - Prob. 13PCh. 7.3 - Prob. 14PCh. 7.3 - Prob. 15PCh. 7.3 - Prob. 16PCh. 7.3 - Prob. 17PCh. 7.3 - Prob. 18PCh. 7.3 - Prob. 19PCh. 7.3 - Prob. 20PCh. 7.3 - Prob. 21PCh. 7.3 - Prob. 22PCh. 7.3 - Prob. 23PCh. 7.3 - Prob. 24PCh. 7.3 - Prob. 25PCh. 7.3 - Prob. 26PCh. 7.3 - Prob. 27PCh. 7.3 - Prob. 28PCh. 7.3 - Prob. 29PCh. 7.3 - Prob. 31PCh. 7.3 - Prob. 32PCh. 7.3 - Prob. 33PCh. 7.3 - Prob. 34PCh. 7.4 - Prove the generalization of Theorem 7.4.1, as...Ch. 7.4 - Prob. 2PCh. 7.4 - Prob. 3PCh. 7.4 - Prob. 4PCh. 7.4 - Prob. 5PCh. 7.4 - Prob. 6PCh. 7.4 - Prob. 7PCh. 7.4 - Prob. 8PCh. 7.4 - Prob. 9PCh. 7.5 - In each of Problems 1 through 6:
Find the general...Ch. 7.5 - Prob. 2PCh. 7.5 - Prob. 3PCh. 7.5 - In each of Problems 1 through 6:
Find the general...Ch. 7.5 - Prob. 5PCh. 7.5 - Prob. 6PCh. 7.5 - Prob. 7PCh. 7.5 - Prob. 8PCh. 7.5 - Prob. 9PCh. 7.5 - Prob. 10PCh. 7.5 - Prob. 11PCh. 7.5 - Prob. 12PCh. 7.5 - Prob. 13PCh. 7.5 - In each of Problems 9 through 14, find the general...Ch. 7.5 - Prob. 15PCh. 7.5 - Prob. 16PCh. 7.5 - Prob. 17PCh. 7.5 - Prob. 18PCh. 7.5 - Prob. 19PCh. 7.5 - Prob. 20PCh. 7.5 - Prob. 21PCh. 7.5 - Prob. 22PCh. 7.5 - Prob. 23PCh. 7.5 - Prob. 24PCh. 7.5 - Prob. 25PCh. 7.5 - Prob. 26PCh. 7.5 - Prob. 27PCh. 7.5 - Prob. 28PCh. 7.5 - Prob. 29PCh. 7.5 - Prob. 30PCh. 7.5 - Prob. 31PCh. 7.5 - Prob. 32PCh. 7.5 - Prob. 33PCh. 7.6 - In each of Problems 1 through 6:
Express the...Ch. 7.6 - Prob. 2PCh. 7.6 - In each of Problems 1 through 6:
Express the...Ch. 7.6 - Prob. 4PCh. 7.6 - In each of Problems 1 through 6:
Express the...Ch. 7.6 - In each of Problems 1 through 6:
Express the...Ch. 7.6 - Prob. 7PCh. 7.6 - Prob. 8PCh. 7.6 - In each of Problems 9 and 10, find the solution of...Ch. 7.6 - Prob. 10PCh. 7.6 - Prob. 11PCh. 7.6 - Prob. 12PCh. 7.6 - Prob. 13PCh. 7.6 - Prob. 14PCh. 7.6 - Prob. 15PCh. 7.6 - Prob. 16PCh. 7.6 - Prob. 17PCh. 7.6 - Prob. 18PCh. 7.6 - Prob. 19PCh. 7.6 - Prob. 20PCh. 7.6 - Prob. 21PCh. 7.6 - Prob. 22PCh. 7.6 - Prob. 23PCh. 7.6 - Prob. 24PCh. 7.6 - Prob. 25PCh. 7.6 - Prob. 26PCh. 7.6 - Prob. 27PCh. 7.6 - Prob. 28PCh. 7.6 - Prob. 29PCh. 7.7 - In each of Problems 1 through 10:
Find a...Ch. 7.7 - Prob. 2PCh. 7.7 - Prob. 3PCh. 7.7 - Prob. 4PCh. 7.7 - Prob. 5PCh. 7.7 - Prob. 6PCh. 7.7 - Prob. 7PCh. 7.7 - Prob. 8PCh. 7.7 - Prob. 9PCh. 7.7 - Prob. 10PCh. 7.7 - Prob. 11PCh. 7.7 - Prob. 12PCh. 7.7 - Prob. 13PCh. 7.7 - Prob. 14PCh. 7.7 - Prob. 15PCh. 7.7 - Prob. 16PCh. 7.7 - Prob. 17PCh. 7.7 - Prob. 18PCh. 7.8 - Prob. 1PCh. 7.8 - Prob. 2PCh. 7.8 - Prob. 3PCh. 7.8 - Prob. 4PCh. 7.8 - Prob. 5PCh. 7.8 - Prob. 6PCh. 7.8 - Prob. 7PCh. 7.8 - Prob. 8PCh. 7.8 - Prob. 9PCh. 7.8 - Prob. 10PCh. 7.8 - Prob. 13PCh. 7.8 - Prob. 14PCh. 7.8 - Prob. 15PCh. 7.8 - Prob. 16PCh. 7.8 - Prob. 17PCh. 7.8 - Prob. 18PCh. 7.8 - Prob. 19PCh. 7.8 - Prob. 20PCh. 7.8 - Prob. 21PCh. 7.8 - Prob. 22PCh. 7.9 - Prob. 1PCh. 7.9 - In each of Problems 1 through 12 find the general...Ch. 7.9 - Prob. 3PCh. 7.9 - Prob. 4PCh. 7.9 - Prob. 5PCh. 7.9 - In each of Problems 1 through 12 find the general...Ch. 7.9 - Prob. 7PCh. 7.9 - Prob. 8PCh. 7.9 - Prob. 9PCh. 7.9 - Prob. 10PCh. 7.9 - In each of Problems 1 through 12 find the general...Ch. 7.9 - Prob. 12PCh. 7.9 - Prob. 13PCh. 7.9 - Prob. 14PCh. 7.9 - Prob. 15PCh. 7.9 - Prob. 16PCh. 7.9 - Prob. 17PCh. 7.9 - Prob. 18P
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