Question: How do you answer 1 given the following axioms? 1. Let S be the set of all non-negative integers. For u, VES define uv= uv

How do you answer 1 given the following axioms?

1. Let S be the set of all non-negative integers. For u, VES define uv= uv and k Ou = ku for any scalar k (for example, 406 =24 and 206=12). Determine if S is a vector space. The vector space axioms are on the back of this sheet. If u and v are objects in I'then u @ v is in V. (closure under addition) uev-YOU (commutative property of addition) ue (vew)-(uvow (associative property of addition) 3 0l' such that 0 u-u @0-u Vuel (additive identity) Vuel' 3 -uel' such that u @ (-u) =(-u)@u-0 (opposites) If k is any scalar and u is any object in ', then Ou is in I' (closure under scalar multiplication) ko (u e) v) = (kou) e (kov) (distributive property) (k +1)Ou= (kou)(lou) (distributive property) ko (lou) = (kl)ou (associative property of multiplication) (multiplicative identity)

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