Prove a few theorems about vector spaces using the axioms

[ataraxia]

Hey guys,

I need to prove a few theorems about vector spaces using the axioms.

a) Prove: if -v = v, then v = 0

b) Prove: (-r)v = -(rv)

c) Prove: r(-v) = -(rv)

d) Prove: v - (-w) = v + w

where r is a scalar and v, w are vectors.

 

[mathwonk]

really, you need to do those yourself.