Let (a,b) and (c,d) be in V and c be in R, we define:

(a,b) + (c,d) = (a+2c,b+3d) and c(a,b) = (ca,cb)

Using the eight properties.

I know that the multiplication is normal, so those properties work, but the addition does not hold under the conditions, does it?

(u + v) + w =/= u + ( v + w)

u + v =/= v + u

-> If u = (a,b) and v = (c,d),

u + v = (a,b) + (c,d) = (a+2c,b+3d)

v + u = (c,d) + (a,b) = (c+2a,d+3b)

So it's not a vector space. Is this correct ??