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3 Suppose V is finite-dimensional and v element of V with v is not equals to 0. Prove that there exists phi element of V? such that phi(v) = 1. Solution As V is finite dimensional, and non zero there exists v\' such that v *v\' =1 (since non zero elements in finite dimensional vector space have multiplicative inverse.) Hence there exists phi in V\' such that phi(v) =1.

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3 Suppose V is finite-dimensional and v element of V with v is not equals to 0. Prove that there exists phi element of V? such that phi(v) = 1. Solution As V is finite dimensional, and non zero there exists v' such that v *v' =1 (since non zero elements in finite dimensional vector space have multiplicative inverse.) Hence there exists phi in V' such that phi(v) =1

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  • 1. 3 Suppose V is finite-dimensional and v element of V with v is not equals to 0. Prove that there exists phi element of V? such that phi(v) = 1. Solution As V is finite dimensional, and non zero there exists v' such that v *v' =1 (since non zero elements in finite dimensional vector space have multiplicative inverse.) Hence there exists phi in V' such that phi(v) =1