Let G = GL2(R). {[ {[ а (a) Prove that T = | a, c, d e R, ad is a subgroup of G. d 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 = c} is not a subgroup of G. C d

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Let G = GL2(R).
{[::
{[:
{[::
a
(a) Prove that T
| a, c, d e R, ad #0} is a subgroup of G.
d
a
(b) Prove that D =
| a, d e R, ad + 0
is a subgroup of G.
а
(c) Prove that S
| a, b, c, d e R, b
is not a subgroup of G.
= C
Transcribed Image Text:Let G = GL2(R). {[:: {[: {[:: a (a) Prove that T | a, c, d e R, ad #0} is a subgroup of G. d a (b) Prove that D = | a, d e R, ad + 0 is a subgroup of G. а (c) Prove that S | a, b, c, d e R, b is not a subgroup of G. = C
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