Let $V=R^3$, and define ${f_1,f_2,f_3} \in V^*$ as follows: $f_1(x,y,z)=x-2y, f_2(x,y,z)=x+y+z$, prove that ${f_1,f_2,f_3}$ is a basis for $V^*$.
I heard that all I need is to prove that ${f_1,f_2,f_3}$ are linearly independent and I can skip through the span part because $dim(V)=dim(V^*)$. Can someone explain why?