3 Suppose V is finitedimensional and v element of V with v i

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