Need help with determining if a set is a vector space.

Let V = {0,1,2} with addition defined by mod 3 and scalar multiplication given by ku=u^{k} mod 3 for all K is an element of real numbers, u is an element of V. Is the set V a vector space?

am I supposed to set u= <u_{1},u_{2},u_{3}> and then go through all the axions to determine whether if it's a vector space?

Re: Need help with determining if a set is a vector space.

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Originally Posted by

**bakinbacon** Let V = {0,1,2} with addition defined by mod 3 and scalar multiplication given by ku=u^{k} mod 3 for all K is an element of real numbers, u is an element of V. Is the set V a vector space?

Are you sure k is a real number? Then 2^{1/2} is not in V.