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Let GL(2,R) be the general linear group of 2 by 2 matrices. 1 x is a) Show that o: R GL (2,R) where o(x) = 1 a homomorphism. b) Determine the kernel of o. c) Determine whether ois one-to-one. d) Determine whether o is onto.

Let GL(2,R) be the general linear group of 2 by 2 matrices. 1 x is a) Show that o: R GL (2,R) where o(x) = 1 a homomorphism. b) Determine the kernel of o. c) Determine whether ois one-to-one. d) Determine whether o is onto.

Advanced Engineering Mathematics
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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Abstract Algebra I
QUESTION 2 Let GL (2,R) be the general linear group of 2 by 2 matrices. 1 x a) Show that o : R GL (2,R) where o(x) =| is 0 1 a homomorphism. b) Determine the kernel of o. c) Determine whether o is one -to-one. d) Determine whether o is onto.
Transcribed Image Text:QUESTION 2 Let GL (2,R) be the general linear group of 2 by 2 matrices. 1 x a) Show that o : R GL (2,R) where o(x) =| is 0 1 a homomorphism. b) Determine the kernel of o. c) Determine whether o is one -to-one. d) Determine whether o is onto.
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