1. The problem statement, all variables and given/known data Determine whether set is a vector space. If not, give at least one axiom that is not satisfied. the set of vectors <a1,a2>, addition and scalar multiplication defined by: <a1,a2>+<b1,b2>=<a1+b1+1,a2+b2+1> k<a1,a2>=<ka1+k-1,ka2+k-1> 3. The attempt at a solution For Vector Addition: 1) well since a1 and a2 is not restricted, the vector spaces are all real entities in V 2) Rule:x+y=y+x; <a1,a2>+<b1,b2>=<a1+b1+1,a2+b2+1>=<b1,b2> 3)Rule:(x+y)+z=(x+(y+z); (<a1,a2>+<b1,b2>)+<0,0>= <a1,a2>+(<b1,b2>+<0,0>) 4)Not sure how to prove is this set has a unique vector O in V such that O+x=x+O 5)Rule: There exist a vector where x+(-x)=(-x)+x=O; Since the set is not restricted, there exist a negative vector where a1+(-a1)=(-a1)+a1 For Scalar Multiplication: 6)Since the set is no restricted, any scalar would be in the space 7)Rule:k(x+y)=kx+ky; Not sure how to prove this one.... 8)Rule: (k1+k2)x=k1x+k2x nor this one 9)Rule:k1(k2x)=(k1k2)x or this one 10)Rule: 1x=x This one obviously satisfies Can someone give me hints on the ones i didn't get and also see if the ones i did is correct?