Let V be the set of all real numbers r such that rx ≥ 0. Define an operation of "addition" by x By = xy + 1 for all x, y € V. Define an operation of "scalar multiplication" by α I I =a²x for all a € R and I EV. Under the operations and the set V (is/is not) a vector space. If it is not, list all the vector space axioms (see 5.1.1 (1)-(10)) which fail to hold. Answer: The axioms which are not satisfied are

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