Hi all,

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: LetXbe a vector in R^n. IfXdotY=0 for every vectorYin R^n, thenX=0.

So the contrapositive is: IfX=/=0, thenXdotY=/=0 for every vectorYin R^n. Right?

But ifYcan be every vector in R^n, then couldn'tYbe the zero vector, henceXdotY=0.

I can't figure out anyway around this fact. I have been specifically told not to alter any restrictions (ie "for every vectorYin R^n") when using the contrapositive.

Thanks in advance.