1. The problem statement, all variables and given/known data Prove (u,v,u+v) can not be a basis for <u,v,u+v>. 2. Relevant equations 3. The attempt at a solution Let αu+βv+γ(u+v)=0 αu+βv=-γ(u+v) α/γ(u)+β/γ(v)=-(u+v) α/γ(u)+β/γ(v)+1*(u+v)=0 Since α/γ,β/γ,1 are not all zeros, therefore, (u,v,u+v) are linearly dependent. Hence it doesn't form basis for <u,v,u+v>. Let me know if this is the right approach towards the proof.