Question: Consider the set V = R with the addition @ and scalar multiplication o defined in the following unusual manner: U1 U2 U2 u2 +

Consider the set V = R with the "addition" @ and "scalar multiplication" o defined in the following unusual manner: U1 U2 U2 u2 + 12 - 1 ko U1 kunth - 1 = U2 kuz - k+1 (i) Find the zero vector 0 for @@, that is, the additive identity. HINT: It is not (ii) Find the vector v = ( $ ) such that v D = 0. HINT: It is not (iii) Prove that IR is a vector space under the operations @ and o defined above, i.e. show that all the axioms are satisfied

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