Determine whether the given set is a vector space If not giv

Determine whether the given set is a vector space. If not, give at least one axiom that is not satisfied. Unless stated to the contrary, assume that vector addition and scalar multiplication are the ordinary operations defined on that set The set of vectors

Solution

because not closed under +, if (a,b) and (x,y) are in given set then sum should be there, but

(a,b) + (x,y)= (a+x, b+y)

=> b+y=3(a+x)+1 not =3(a+x)+2