1. The problem statement, all variables and given/known data The set R^2 with addition defined by <x,y>+<a,b>=<x+a+1,y+b>, and scalar multiplication defined by r<x,y>= <rx+r-1,ry>. The answer in the back of the book says it is a vector space, but I am having trouble proving that 0+v=v and v+(-v)=0 2. Relevant equations 3. The attempt at a solution My guess is that you take v+(-1)v=0, applying the above definition of scalar multiplication to (-1)v, which gives 0=<-1,0>. Using that definition of 0, then 0+v=v, but I'm not sure if any of that is correct.