Sorry, couple of typo's in there. I think i understand the original question now, many thanks to you!
Ok so for 2nd, H= (ax|dy) for ad=1 ?!
Do all elements of G preserve each of the two asymptotes of ¬ ?
What extent will results apply to the groups G' = G(¬') preserving other...
If x'y'=xy=1
Comparing coefficients:
ac=0
bd=0
ad+bc=1
& as detA ≠ 0, ad-bc ≠ 0
Either a=0 & d=0 or b=0 & c=0
So elements of G:
( ax ) ,( by )
( dy ) ( cx )
Correct?!
Further please, let H be the subgroup of G preserving each of the two branches of ¬. Determine the index of H in G...
Thank you Billy Bob, glad to be here!
OK
Definition:
an affine transformation f of Rn is any transformation of the form
f A,t : x -> Ax + t
where A is an invertible n×n matrix; detA = 0, and t is an element of Rn.
so ??
x' = ax+by+t1
y' = cx+dy+t2
x'y'=acx2+(ad...
Homework Statement
For any subset ¬ of the affine plane R^2, let G(¬) denote the group of all affine transformations f of R^2 such that f(¬) = ¬.
Exercise: Find all the elements of the group G = G(¬), where ¬ is the hyperbola xy = 1
in R^2.
The Attempt at a Solution
Hey! I'm afraid I’m...