Mathematics for Machine Technology
7th Edition
ISBN: 9781133281450
Author: John C. Peterson, Robert D. Smith
Publisher: Cengage Learning
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Chapter 57, Problem 76A
Find the unknown area, height, or base for each of the trapezoids 65 through 76. Where necessary, round the answers to 1 decimal place.
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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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(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 57 Solutions
Mathematics for Machine Technology
Ch. 57 - Trace this line segment two times. On one copy...Ch. 57 - Find the length of x. Round the answer to 2...Ch. 57 - Prob. 3ACh. 57 - Prob. 4ACh. 57 - Prob. 5ACh. 57 - Prob. 6ACh. 57 - Prob. 7ACh. 57 - Prob. 8ACh. 57 - Prob. 9ACh. 57 - Prob. 10A
Ch. 57 - Prob. 11ACh. 57 - Prob. 12ACh. 57 - Prob. 13ACh. 57 - Express each area as indicated. Round each answer...Ch. 57 - Prob. 15ACh. 57 - Prob. 16ACh. 57 - Prob. 17ACh. 57 - Prob. 18ACh. 57 - Prob. 19ACh. 57 - Prob. 20ACh. 57 - Prob. 21ACh. 57 - Prob. 22ACh. 57 - Prob. 23ACh. 57 - Prob. 24ACh. 57 - Prob. 25ACh. 57 - Prob. 26ACh. 57 - Prob. 27ACh. 57 - Prob. 28ACh. 57 - Prob. 29ACh. 57 - Prob. 30ACh. 57 - Prob. 31ACh. 57 - Prob. 32ACh. 57 - Prob. 33ACh. 57 - Prob. 34ACh. 57 - Prob. 35ACh. 57 - Prob. 36ACh. 57 - Prob. 37ACh. 57 - Prob. 38ACh. 57 - Prob. 39ACh. 57 - Prob. 40ACh. 57 - Prob. 41ACh. 57 - Prob. 42ACh. 57 - Prob. 43ACh. 57 - Prob. 44ACh. 57 - Prob. 45ACh. 57 - Prob. 46ACh. 57 - Prob. 47ACh. 57 - Prob. 48ACh. 57 - Prob. 49ACh. 57 - Prob. 50ACh. 57 - Prob. 51ACh. 57 - Prob. 52ACh. 57 - Prob. 53ACh. 57 - Prob. 54ACh. 57 - Prob. 55ACh. 57 - Prob. 56ACh. 57 - Prob. 57ACh. 57 - Prob. 58ACh. 57 - Prob. 59ACh. 57 - Prob. 60ACh. 57 - Prob. 61ACh. 57 - Prob. 62ACh. 57 - Prob. 63ACh. 57 - Prob. 64ACh. 57 - Prob. 65ACh. 57 - Prob. 66ACh. 57 - Prob. 67ACh. 57 - Prob. 68ACh. 57 - Prob. 69ACh. 57 - Prob. 70ACh. 57 - Prob. 71ACh. 57 - Prob. 72ACh. 57 - Prob. 73ACh. 57 - Prob. 74ACh. 57 - Find the unknown area, height, or base for each of...Ch. 57 - Find the unknown area, height, or base for each of...Ch. 57 - A cross section of an aluminum bar in the shape of...Ch. 57 - Prob. 78ACh. 57 - Prob. 79ACh. 57 - One of the examples showed how to find the area of...
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