Let V be the set of all ordered pairs of real numbers under the following operations of addition 1. and scalar multiplication. Define addition and scalar multiplication on V as follows: (a, b) + (c,d) = (a + c −6, b + d + 1) and k(a, b) = (ka, kb) a. There exists a zero vector 0 in V such that for any v in V, 0 + v = v + 0 = v. Which ordered pair in V is the zero vector? b. V is not a vector space. Determine one of the vector space axioms that is not satisfied by V, and demonstrate with a counterexample.

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