Mathematics For Machine Technology
8th Edition
ISBN: 9781337798310
Author: Peterson, John.
Publisher: Cengage Learning,
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Question
Chapter 76, Problem 1A
To determine
To find the length of the diagonal
Expert Solution & Answer
Answer to Problem 1A
Explanation of Solution
Given information:
We are given the following figure-
Calculation:
After observing the figure closely and then writing the relation to calculate the length of diagonal
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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 76 Solutions
Mathematics For Machine Technology
Ch. 76 - Prob. 1ACh. 76 - Prob. 2ACh. 76 - Prob. 3ACh. 76 - Prob. 4ACh. 76 - Prob. 5ACh. 76 - Prob. 6ACh. 76 - Prob. 7ACh. 76 - Prob. 8ACh. 76 - Prob. 9ACh. 76 - Prob. 10A
Ch. 76 - Prob. 11ACh. 76 - Prob. 12ACh. 76 - Prob. 13ACh. 76 - In each Exercises 13 through 16, the top, front,...Ch. 76 - In each Exercises 13 through 16, the top, front,...Ch. 76 - Prob. 16ACh. 76 - Prob. 17ACh. 76 - In each of the following exercises, the top,...Ch. 76 - Prob. 19ACh. 76 - Prob. 20ACh. 76 - Prob. 21ACh. 76 - Prob. 22A
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