Hello. I have just started doing proofs involving Linear Algebra and I need some guidance and a little push in the right direction. Here is the result I am trying to prove:

Let V be a vector space containing nonzero vectors u and v. Prove that if u

v for each

, then u

(u + v) for each

.

Now I am thinking I can prove this using the contrapositive. I believe the contrapositive is: If u =

(u+v) for some

, then u =

v for some

.

If this is the correct negation then I know that u =

(u+v) =

u+

v so I need to find a way to make

u+

v =

v. Im not quite sure how to go about doing this so I am hoping someone here can push me in the right direction. Thanks