1. ## Help with proof

This is a simple proof, and it makes sense logically, but I don't know how to show it. Any tips on how to prove stuff like this?

if V is a vector space with basis {v1,...,vn} and W is a subspace of V = sp(v3,..,vn)
show that if w E W and w = r1v1 + r2v2 for r1,r2 E R, then w = 0.

Well since V has a basis of v1...vn, that means that sp(v1...vn) = V.
All vectors in W can be written by a linear combination of v3...vn, thus if w is a linear combination of v1 and v2, and lies in W, that implies that it is the zero vector.

2. ## Re: Help with proof

Originally Posted by Kuma
All vectors in W can be written by a linear combination of v3...vn, thus if w is a linear combination of v1 and v2, and lies in W, that implies that it is the zero vector.
Yes, but how exactly is this implied? If $w=r_1v_1+r_2v_2=r_3v_3+\dots+r_nv_n$, then $-r_1v_1-r_2v_2+r_3v_3+\dots+r_nv_n=0$, so...