Problem 1. Let D₁ = {e,0, 0², 0³, T₁07, 0²7,0³T). Let H = (0²) = {e,o²}. (a) List the left cosets of H in D₂. (b) List the right cosets of H in D₁. (c) Prove that H is normal in D₁. (d) Construct an isomorphism f: D/H → Z₂x Z₂. The group structure on the right is componentwise addition modulo 2.
Problem 1. Let D₁ = {e,0, 0², 0³, T₁07, 0²7,0³T). Let H = (0²) = {e,o²}. (a) List the left cosets of H in D₂. (b) List the right cosets of H in D₁. (c) Prove that H is normal in D₁. (d) Construct an isomorphism f: D/H → Z₂x Z₂. The group structure on the right is componentwise addition modulo 2.
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Linear Transformations
Section6.1: Introduction To Linear Transformations
Problem 45E: Let T be a linear transformation from R2 into R2 such that T(x,y)=(xcosysin,xsin+ycos). Find a...
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![Problem 1. Let D₁ = {0,0,0²,0³¹, T₁0T₁ 0²7,0³7}. Let H = (0²) = {c,o²}.
(a) List the left cosets of H in D₁.
(b) List the right cosets of H in D₁.
(c) Prove that H is normal in D₁.
(d) Construct an isomorphism f: D/H → Z₂x Z₂. The group structure on the right is
componentwise addition modulo 2.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F91132889-1af9-4aa6-8228-e0491323cb80%2Fb430d0b8-fad5-4f10-bd94-1181bc20fed3%2Fbzczsxs_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Problem 1. Let D₁ = {0,0,0²,0³¹, T₁0T₁ 0²7,0³7}. Let H = (0²) = {c,o²}.
(a) List the left cosets of H in D₁.
(b) List the right cosets of H in D₁.
(c) Prove that H is normal in D₁.
(d) Construct an isomorphism f: D/H → Z₂x Z₂. The group structure on the right is
componentwise addition modulo 2.
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