- #1
YABSSOR
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1. Which of the following is a group?
To find the identity element, which in these problems is an ordered pair (e1, e2) of real numbers, solve the equation (a,b)*(e1, e2)=(a,b) for e1 and e2.
2. (a,b)*(c,d)=(ac-bd,ad+bc), on the set ℝxℝ with the origin deleted.
3. The question also asks for you to find the inverse and I think implicitly for associativity and then for commutativity. I've got the other three down, but the identity axiom is giving me trouble.
(a,b)*(a,b)-1=(aa-1-bb-1,ab-1+ba-1)
Unless I'm really screwing up here, I think this implies that e1-e2 is the first value, which would be equivalent to e1. However, I don't know how to resolve the ab-1+ba-1) part.
I think I've been dropped from this class for a lack of prerequisites, but I think I'm still going to try and finish the class nonetheless.
To find the identity element, which in these problems is an ordered pair (e1, e2) of real numbers, solve the equation (a,b)*(e1, e2)=(a,b) for e1 and e2.
2. (a,b)*(c,d)=(ac-bd,ad+bc), on the set ℝxℝ with the origin deleted.
3. The question also asks for you to find the inverse and I think implicitly for associativity and then for commutativity. I've got the other three down, but the identity axiom is giving me trouble.
(a,b)*(a,b)-1=(aa-1-bb-1,ab-1+ba-1)
Unless I'm really screwing up here, I think this implies that e1-e2 is the first value, which would be equivalent to e1. However, I don't know how to resolve the ab-1+ba-1) part.
I think I've been dropped from this class for a lack of prerequisites, but I think I'm still going to try and finish the class nonetheless.