(a) Show that the set of strictly positive reals: R(positive) = { a E R | a > 0}, provided with the operations defined below is a vector space: - Addition: a + b = ab for all a, b E R(positive) - Multiplication by a scalar: k*a=a^k, for all k E R and a E R (positive) (b) Why is the set of positive reals { a E R | a ⩾ 0}, endowed with the same operations, is not a vector space?

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