2. A set of objects is given together with operations fo addition and scalar multiplication. Determine if the set is a vector space (justify your decision). Furthermore, if the set is not a vector space, list all axioms that fail to hold with justification. (a) The set of al pairs of real numbers (a, y) with the operations (21, y1) + (x2, 92) = (21 + 22, 31 + 32) and k(x1, y1) = (2kx1, 2kyl). (b) W = {(x,0) : E R) with the standard operations on RR2. (c) V = {a : a > 0} with the operations a + a' = aa' and ka = ak. (d) M = {le :a,be R with standard matrix addition and scalar multiplication. (e) The set of all real-valued function defined on R with the operations (f +g)(x) = f(x) +g(x) and kf(x) = f(x + k)