Answer Happy

Determine whether the set equipped with the given operations is a vector space. For those that are not vector spaces identify the vector space axioms that fail. The set of all pairs of real numbers of the form (3,x) with the operations (33+ (3) (3, y) + (3, y') = (3, y + y) (, k(3, y) = (3, ky) = O V is not a vector space, and Axioms 1, 2, 3 fail to hold. O V is not a vector space, and Axiom 4 fails to hold. O V is a vector space. O V is not a vector space, and Axioms 4 and 5 fail to hold. O Vis not a vector space, and Axioms 8 and 9 fail to hold.