oh ok, i was just trying anything really.
my biggest problem is using ||f(u) - f(v)|| = ||u - v||
to show that f(u) x f(v) = +- f(u x v)
i just don't know how to relate the two,
I don't want you to give me the answer AKG, i would much rather understand what i am suppose to do then get...
Ok I know that isometries preserve distance and in order for a fn to be an isometry || f(u) - f(v) || = || u - v ||
and in this question it asks to prove
prove that if an isometry satisfies f(0) = 0 then we have
f(u) x f(v) = +- f(u x v)
and what property of f determines the choice of...
f(v) = (the matrix)
|cosx sinx |
|sinx -cosx |(v)
If x is in R and f: R^2 --> R^2
show that f is a reflection in a line L through the origin, and find the line of reflection.
im having trouble figureing this out, i know that i need to find a line L fixed by f, and then to...