Originally Posted by

**CropDuster** 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: Let **X** be a vector in R^n. If **X**dot**Y**=0 for every vector **Y** in R^n, then **X**=**0**.

So the contrapositive is: If **X**=/=**0**, then **X**dot**Y**=/=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 **X**dot**Y**=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.