Let ?V be the set of vectors in ?2R2 with the followingdefinition of addition and scalar multiplication:
Addition: [?1?2]?[?1?2]=[0?2+?2][x1x2]?[y1y2]=[0x2+y2]
Scalar Multiplication: ??[?1?2]=[0??2]??[x1x2]=[0?x2]
Determine which of the Vector Space Axioms are satisfied.
A1. ???=???x?y=y?x for any ?x and ?y in ?V
? YES NO
A2. (???)??=??(???)(x?y)?z=x?(y?z) for any ?,?x,y and ?z in?V
? YES NO
A3. There exists an element 00 in ?V such that ??0=?x?0=x foreach ???x?V
? YES NO
A4. For each ???x?V, there exists an element  ???x in?V such that ??(??)=0x?(?x)=0
? YES NO
A5.  ??(???)=(???)?(???)??(x?y)=(??x)?(??y) for eachscalar ?? and any ?x and ?y ?V
? YES NO
A6. (?+?)??=(???)?(???)(?+?)?x=(??x)?(??x) for any scalars ??and  ?? and any ???x?V
? YES NO
A7. (??)??=??(???)(??)?x=??(??x) for any scalars ??and  ?? and any ???x?V
? YES NO
A8. 1??=?1?x=x for all ???x?V
? YES NO
