Determine whether the following set with the standard operations, is a vector space. If it is not, then determine the set of axioms that it fails. {(x, x): x is a real number) O This set is not a vector space. It fails the following axioms. Additive identity Additive inverse Associative property Scalar identity O This set is a vector space. All ten vector space axioms hold. O This set is not a vector space. It fails the following axioms. Scalar identity Associative property Distributive property Additive identity O This set is not a vector space. It fails the following axioms. Closer under addition Closer under scalar multiplication O This set is not a vector space. It fails the following axionms. Commutative property Additive identity Distributive property

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