3. Let V be the set of ordered pairs (a, b) of real numbers. Show that V is not a vector space over R with addition and scalar multiplication defined by: (i) (a, b) + (c,d) = (a +d,b+c) and k(a, b) = (ka, kb), (ii) (a, b) + (c,d) = (a + c,b+d) and k(a, b) = (a, b), (a, b) + (c,d) = (0,0) and k(a, b) = (ka, kb), (a, b) + (c,d) = (ac, bd) and k(a, b) = (ka, kb). (iii) (iv)

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