1. Let T be a group of all invertible 2 x2 matrices of the form Where a.b.C ER and ac+0. Let / be the set of matrices of the form 0 1 where x ER. a. Prove that U is a subgroup of T. b. Determine whether U is a normal subgroup of T. 2. Let G be a group. Prove or disprove that z= {XE G: xg = gx for all ge G} is a Subgroup of G .

1. Let T be a group of all invertible 2 x2 matrices of the form Where a.b.C ER and ac+0. Let / be the set of matrices of the form 0 1 where x ER. a. Prove that U is a subgroup of T. b. Determine whether U is a normal subgroup of T. 2. Let G be a group. Prove or disprove that z= {XE G: xg = gx for all ge G} is a Subgroup of G .

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

100%

1. Let T be a group of all invertible 2 x2 matrices of the form
Where a.b.C ER and ac+0. Let / be the set of matrices of the form
0 1
where x ER.
a. Prove that U is a subgroup of T.
b. Determine whether U is a normal subgroup of T.
2. Let G be a group. Prove or disprove that z= {XE G: xg = gx for all ge G} is a
Subgroup of G .

a b
2.3 Let e: (M2(R), + )→ <R, +) be defined by e
|= a + d. where a,b,c,d ER
(a) Prove that e is a homomorphism.
(b) Determine Ker 0 ·

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