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**Twinsfan85** 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 $\displaystyle \neq$ $\displaystyle \alpha$v for each $\displaystyle \alpha \in \mathbb{R}$, then u $\displaystyle \neq$ $\displaystyle \beta$(u + v) for each $\displaystyle \beta \in \mathbb{R}$.

Now I am thinking I can prove this using the contrapositive. I believe the contrapositive is: If u = $\displaystyle \beta$(u+v) for some $\displaystyle \beta \in \mathbb{R}$, then u = $\displaystyle \alpha$v for some $\displaystyle \alpha \in \mathbb{R}$.

If this is the correct negation then I know that u = $\displaystyle \beta$(u+v) = $\displaystyle \beta$u+$\displaystyle \beta$v so I need to find a way to make $\displaystyle \beta$u+$\displaystyle \beta$v = $\displaystyle \alpha$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