Let G = GL2(R). {[: {[ {[:: a (a) Prove that T = | a, c, d e R, ad #0} is a subgroup of G. d а (b) Prove that D= | a, d e R, ad # 0 is a subgroup of G. d a (c) Prove that S = | a, b, c, d E R, b = c is not a subgroup of G. a (d) Determine whether A = | a, b e R} is a subgroup of G. {[:: {[: : (e) Determine whether B = | b, c eR is a subgroup of G. (f) Determine whether C = |de R, d+ is a subgroup of G. d
Let G = GL2(R). {[: {[ {[:: a (a) Prove that T = | a, c, d e R, ad #0} is a subgroup of G. d а (b) Prove that D= | a, d e R, ad # 0 is a subgroup of G. d a (c) Prove that S = | a, b, c, d E R, b = c is not a subgroup of G. a (d) Determine whether A = | a, b e R} is a subgroup of G. {[:: {[: : (e) Determine whether B = | b, c eR is a subgroup of G. (f) Determine whether C = |de R, d+ is a subgroup of G. d
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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please just answer d,e &f
![Let G =
GL2(R).
{[::]
{[:
{[::
{[
{
a
(a) Prove that T
| a, c, d e R, ad 70
is a subgroup of G.
=
a
(b) Prove that D =
| a, d e R, ad + 0 } is a subgroup of G.
0 d
a
(c) Prove that S =
| a, b, c, d e R, b
is not a subgroup of G.
= C
C
d
a
(d) Determine whether A
| a, b e R} is a subgroup of G.
(e) Determine whether B =
| b, c eR} is a subgroup of G.
1
(f) Determine whether C =
|d e R, d +0} is a subgroup of G.
0 d](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdb708fa5-116d-42c3-bb62-31dd00678e29%2Fc3942808-e234-4395-a811-859436a401bf%2F8nxdxd_processed.png&w=3840&q=75)
Transcribed Image Text:Let G =
GL2(R).
{[::]
{[:
{[::
{[
{
a
(a) Prove that T
| a, c, d e R, ad 70
is a subgroup of G.
=
a
(b) Prove that D =
| a, d e R, ad + 0 } is a subgroup of G.
0 d
a
(c) Prove that S =
| a, b, c, d e R, b
is not a subgroup of G.
= C
C
d
a
(d) Determine whether A
| a, b e R} is a subgroup of G.
(e) Determine whether B =
| b, c eR} is a subgroup of G.
1
(f) Determine whether C =
|d e R, d +0} is a subgroup of G.
0 d
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