Proving something is a vector space

[PsychonautQQ]

Homework Statement

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

Homework Equations

None

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?

 

[vela]

Yeah, I think it's a typo. You should check with your professor.