Let U be a finite dimensional vector space over F

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answerhappygod
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Let U be a finite dimensional vector space over F

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Let U be a finite dimensional vector space over F and u #0 be any vector of U. Then there exists some fe U* such that f(u) = 0



Since U is a finite-dimensional vector space, then it has a maximum linearly independent subset, which we shall call, BCU , and this basis generates U. Also, if for every * UEU we had f(u) = 0 then we would see that it would be the null space and U ER but we had said earlier that U is finite-dimensional so it contradicts that, and so there must be at least one such that f(u) +0
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