Show how the axioms for a vector space V can be used to prove the elementary properties described after the definition of a vector space. Fill in the blanks with the appropriate axiom numbers. Because of Axiom 2, Axioms 4 and 5 imply, respectively, that 0 + u = u and - u + u = 0 for all u.

Fill in the missing axiom numbers in the following proof that c0 = 0 for every scalar c.

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c0 = c(0+0) =c0 + co Add the negative of c0 to both sides: c0 +(−c0) = [c0 +c0]+(−c0) c0 +(−c0) = c0+[c0+(−c0)] 0 =c0 +0 0 = c0 by Axiom by Axiom by Axiom by Axiom. by Axiom. (a) (b) (c) (d) (e)