So I've just started a linear algebra course, and this is my first exposure to formal proofs.
Here is a question from my book:
Prove the following by contrapositive: Let X be a vector in R^n. If XdotY=0 for every vector Y in R^n, then X=0.
So the contrapositive is: If X=/=0, then XdotY=/=0 for every vector Y in R^n. Right?
But if Y can be every vector in R^n, then couldn't Y be the zero vector, hence XdotY=0.
I can't figure out anyway around this fact. I have been specifically told not to alter any restrictions (ie "for every vector Y in R^n") when using the contrapositive.
Thanks in advance.