- #1
mattmns
- 1,128
- 6
I have a problem that states
Define the Special linear group by: (Let R denote real numbers)
[tex]SL(2,R) = \{ A\in GL(2,R): det(A)=1\}[/tex]
Prove that SL(2,R) is a subgroup of GL(2,R).
___
Now a subset H of a group G is a subgroup if:
i) [tex]1 \in H[/tex]
ii) if [tex] x,y \in H[/tex], then [tex]xy \in H[/tex]
iii) if [tex]if x\in H[/tex], then [tex]x^{-1} \in H[/tex]
I have very little knowledge of matricies and I don't even see how 1 could be in SL(2,R), other than maybe something saying that GL(2,R) has 1, so SL(2,R) must have it too, but I bet there is a more appropriate way.
Also what would H be here? Would it a set containing matricies or numbers?
Define the Special linear group by: (Let R denote real numbers)
[tex]SL(2,R) = \{ A\in GL(2,R): det(A)=1\}[/tex]
Prove that SL(2,R) is a subgroup of GL(2,R).
___
Now a subset H of a group G is a subgroup if:
i) [tex]1 \in H[/tex]
ii) if [tex] x,y \in H[/tex], then [tex]xy \in H[/tex]
iii) if [tex]if x\in H[/tex], then [tex]x^{-1} \in H[/tex]
I have very little knowledge of matricies and I don't even see how 1 could be in SL(2,R), other than maybe something saying that GL(2,R) has 1, so SL(2,R) must have it too, but I bet there is a more appropriate way.
Also what would H be here? Would it a set containing matricies or numbers?