
Mathematics For Machine Technology
8th Edition
ISBN: 9781337798310
Author: Peterson, John.
Publisher: Cengage Learning,
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Chapter 86, Problem 19A
To determine
Conversion of BCD (8421) numbers 111 0110.0100 to a decimal numbers.
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Define f: ZZ and 9: ZZ by f(x)=3x+1 and g(x) = x².
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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…
Chapter 86 Solutions
Mathematics For Machine Technology
Ch. 86 - Prob. 1ACh. 86 - Prob. 2ACh. 86 - Prob. 3ACh. 86 - Prob. 4ACh. 86 - Prob. 5ACh. 86 - Prob. 6ACh. 86 - Prob. 7ACh. 86 - Prob. 8ACh. 86 - Prob. 9ACh. 86 - Express the following decimal numbers as BCD...
Ch. 86 - Prob. 11ACh. 86 - Prob. 12ACh. 86 - Prob. 13ACh. 86 - Prob. 14ACh. 86 - Prob. 15ACh. 86 - Prob. 16ACh. 86 - Prob. 17ACh. 86 - Prob. 18ACh. 86 - Prob. 19ACh. 86 - Prob. 20ACh. 86 - Prob. 21ACh. 86 - Express the following BCD (8421) numbers as...Ch. 86 - Express the following decimal numbers as 2421 code...Ch. 86 - Prob. 24ACh. 86 - Prob. 25ACh. 86 - Prob. 26ACh. 86 - Prob. 27ACh. 86 - Express the following 2421 code numbers as decimal...Ch. 86 - Prob. 29ACh. 86 - Prob. 30ACh. 86 - Express the following decimal numbers as 5211 code...Ch. 86 - Prob. 32ACh. 86 - Express the following decimal numbers as 5211 code...Ch. 86 - Prob. 34ACh. 86 - Prob. 35ACh. 86 - Prob. 36ACh. 86 - Prob. 37ACh. 86 - Prob. 38ACh. 86 - Prob. 39ACh. 86 - Prob. 40ACh. 86 - Prob. 41ACh. 86 - Express the following decimal numbers as Excess-3...Ch. 86 - Prob. 43ACh. 86 - Prob. 44ACh. 86 - Prob. 45ACh. 86 - Prob. 46A
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