a subset B of V is called a basis for V if B is linear independent over F and B spans V.

suppose is basis, then there is no such that av1+bv2+cv3=0 unless a,b,c =0

is T a basis?

let

av1+bv2+cv3+d(v1+v2)=0

since V1 and V2 are in V hence d(v1+v2)= dv1+dv2

then we have (a+d)v1+(b+d)v2+cv3=0

clearly if a+d=0, then a need not to be 0 it could be -d