1. The problem statement, all variables and given/known data Consider the set V = R^2 (two dimensions of real numbers) with the following operations of vector addition and scalar multiplication: (x,y) + (z,w) = (x+y-1, y+z) a(x,y) = (ax-a+1,ay) Show that V is a vector space 2. Relevant equations None 3. The attempt at a solution So the first axiom of a vector space is showing that the scalar addition is commutative. However, to me it seems like given the wonky definition of vector addition it is not commutative. (x,y) + (z,w) = (x+y-1, y+z) (z,w) + (x,y) = (z+w-1, w+x) These are only equal to each other if x=z and y=w. Do ya'll think this is a typo?