Consider the multiplicative group GL(2, R), the general linear group of order 2 over R, and the multiplicative group R* of non-zero real numbers. Define bc. Show that GL(2,R) R* by o a b ([ å å ]) C d = ad is an homomorphism, and find kero. Is o an epimorphism? Is ó a monomorphism?

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Consider the multiplicative group GL(2, R), the general
linear group of order 2 over R, and the multiplicative
group R of non-zero real numbers. Define cp:
**
a b
GL(2,R)
->
R by p([
]) ad bc. Show that p is
c d
an homomorphism, and find kerp. Is cp an
epimorphism? Is op a monomorphism?
Consider the multiplicative group GL(2, R), the general linear group
of order 2 over R, and the multiplicative group R* of non-zero real
numbers. Define o GL(2,R) → R* by o
a b
d
• ([ a å ] )
= ad -
bc. Show that is an homomorphism, and find ker o. Is o an
epimorphism? Is ó a monomorphism?
Transcribed Image Text:Consider the multiplicative group GL(2, R), the general linear group of order 2 over R, and the multiplicative group R of non-zero real numbers. Define cp: ** a b GL(2,R) -> R by p([ ]) ad bc. Show that p is c d an homomorphism, and find kerp. Is cp an epimorphism? Is op a monomorphism? Consider the multiplicative group GL(2, R), the general linear group of order 2 over R, and the multiplicative group R* of non-zero real numbers. Define o GL(2,R) → R* by o a b d • ([ a å ] ) = ad - bc. Show that is an homomorphism, and find ker o. Is o an epimorphism? Is ó a monomorphism?
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