Let v r and define fi.f2.fs e v° as follows aa,y,z) =x+y, f2(x,y, 2) = x-2y +z, fi(x,y,z) 3z. prove that {f1 f2. f3} is a basis for v", and then find a basis fo

Let V R and define fi.f2.fs E V° as follows Aa,y,z) =x+y, f2(x,y, 2) = x-2y +z, fi(x,y,z) 3z. Prove that {f1 f2. f3} is a basis for V", and then find a basis for V for which it is the dual basis.