Mathematics for Machine Technology
7th Edition
ISBN: 9781133281450
Author: John C. Peterson, Robert D. Smith
Publisher: Cengage Learning
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Chapter 42, Problem 1A
Write the expression "A number divided by 7 plus twice the number equals 75" as an equation with the unknown as x.
Expert Solution & Answer
To determine
To convert:
The given word statement in the form of a numerical equation.
Answer to Problem 1A
Explanation of Solution
Given:
A number divided by 7 plus twice the number equals 75.
Let 'x' be the unknown number then the equation is written as:
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Let A be a vector space with basis 1, a, b. Which (if any) of the following rules
turn A into an algebra? (You may assume that 1 is a unit.)
(i) a² = a, b² = ab = ba = 0.
(ii) a²=b, b² = ab = ba = 0.
(iii) a²=b, b² = b, ab = ba = 0.
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= 1. Show
(a) Let G = Z/nZ be a cyclic group, so G = {1, 9, 92,...,g" } with g":
that the group algebra KG has a presentation KG = K(X)/(X” — 1).
(b) Let A = K[X] be the algebra of polynomials in X. Let V be the A-module
with vector space K2 and where the action of X is given by the matrix
Compute End(V) in the cases
(i) x = p,
(ii) xμl.
(67) ·
(c) If M and N are submodules of a module L, prove that there is an isomorphism
M/MON (M+N)/N.
(The Second Isomorphism Theorem for modules.)
You may assume that MON is a submodule of M, M + N is a submodule of L
and the First Isomorphism Theorem for modules.
Chapter 42 Solutions
Mathematics for Machine Technology
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