Let G and H be the following subgroups of GL(2; R):

Let G and H be the following subgroups of GL(2, R):

G ={ [a b,0 1 ] | a and b are in R and a is not equal to 0} and H={ [1 b ,0 1 ] | b is in R}

:

(a) Prove that H is normal in G.

(b) Use the First Isomorphism Theorem to prove that G=H is isomorphic to R the

group of nonzero real numbers under multiplication.

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Re: Let G and H be the following subgroups of GL(2; R):

Hi,

I hope maybe by now you have been able to prove the result. However, here is a solution with just a couple of details omitted:

Attachment 28446