Is the Set of Ordered Pairs of Real Numbers a Vector Space Over Reals?

[Punkyc7]

vector space?

Let v denote the set of order pairs of real numbers. If(a1,a2) and (b1,b2) are elements of V and c is an element of the reals, define (a1,a2)+(b1,b2)=(a1+b1,a2b2) and
c(a1,a2)=(ca1,a2)


is v a vector space over reals with these operations?

im thinking its not because the c only goes to a1

or because if a2=0 then there's no element in b2 that makes 1

 

[lanedance]

satrt by listing the vector space axioms and see if the operations satisfy them