We are considering a transformation $f: E^2 \rightarrow E^2$. I need to determine if f is linear and if so, I need to describe its null space and range, and compute its nullity and rank.
$f$ is defined such that it maps each point $(x,y)$ onto its reflection with respect to a fixed line through the origin.
I think I know how to show that is a linear transformation, however, I am having trouble expressing $f(x,y)=\space ?$
Can someone just express for me $f(x,y)$ and explain to me why it has this expression. I can continue from there.