Vector proof

[jsbeckton]

Not looking for the whole anwser here, just a push.

Let V be a vector space over F.

Prove that for any $\displaystyle \vec v{\rm } \in {\rm V, - }\vec v = - 1\vec v$

I started with this:
v=<a,b,c>
-v=<-a,-b,-c>
(-1)v=<(-1)a,(-1)b,(-1)c>
-1v=<-a,-b,-c>

But this seems much to trivial for a proof.

Thanks

 

[pka]

It may “seem much to trivial” but it is a proof.

 

[jsbeckton]

Thanks, sometimes it just seems to simple to be true.