Hey, how was this solved please? Thanks.
hey all,
i have been given this question and i dont have a clue where to start
For any subset ¬of the affine plane R2, let G(¬) denote the group of all affine transformations
fof R2 such that f(¬) = ¬.
1)Find all the elements of the group G = G(¬), where ¬is the hyperbola xy = 1
in R2.
thanks
i managed to do it myself in the end.
you have the form xy=1.
so using affine geometry you can also write this as
x->Ax+b, where A is a 2x2 matrix with abcd as coefficients and uv as t
then
(ax+by+u)(cx+dy+v)=1
now if you expand out and compare coefficients, you two cases.
a=0 or c=0, follow through for this and you will get two matrices as your answer.