Problem 3. In this problem, we will write [b] for the element [b] € Z/kZ.3.1. Show that the map: Z/mnZ(Z/mZ) × (Z/nZ), 4([a]mn) = ([a]m, [a]n)is well-defined, and is a group homomorphism.3.2. Now suppose in addition that m and n are relatively prime. Determine ifis an isomorphism.3.3. If m and n are not relatively prime, can be an isomorphism?4

1) 2) When m and n are relatively prime, by the Chinese Remainder Theorem, there is a bijective…

Answered: Problem 3. In this problem, we will…

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter7: Eigenvalues And Eigenvectors

Section7.CM: Cumulative Review

Problem 16CM

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Find the kernel of the linear transformation T:R4R4, T(x1,x2,x3,x4)=(x1x2,x2x1,0,x3+x4).
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1.15. Write out the following tables for Z/mZ and (Z/mZ)*, as we did in Figur and 1.5. Exercises Fit to page (a) Make addition and multiplication tables for Z/3Z. (b) Make addition and multiplication tables for Z/6Z. (c) Make a multiplication table for the unit group (Z/9Z)*. (d) Make a multiplication table for the unit group (Z/16Z)*.
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