a b1. Let T be a group of all invertible 2 ×2 matrices of the form1 xWhere a,b,c €R and ac#0. Let u be the set of matrices of the form0 1whereχER.a. Prove that U is a subgroup of T .b. Determine whether U is a normal subgroup of T.

Answered: Image /qna-images/answer/d644c76b-27ab-4a2b-ac8e-d8ec211b61f5.jpg

Answered: a b 1. Let T be a group of all…

a b 1. Let T be a group of all invertible 2 x 2 matrices of the form 0 c 1 x 0 1 re a,b,c €R and ac+0. Let u be the set of matrices of the form

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter3: Groups

Section3.5: Isomorphisms

Problem 5E

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Question

a b
1. Let T be a group of all invertible 2 ×2 matrices of the form
1 x
Where a,b,c €R and ac#0. Let u be the set of matrices of the form
0 1
where
χER.
a. Prove that U is a subgroup of T .
b. Determine whether U is a normal subgroup of T.

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