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> 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 $V^\*$.
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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?