You should show specifically: if u= (a,b), v= (c,d), and w= (e, f) then u+ v= (a+2c, b+3d) and then (u+ v)+ w= (a+2c+ 2u, b+3d+ 3f) while v+w= (c+2e, d+ 3f) and u+ (v+w)= (a+ 2(c+3e),b+3(d+3f))= (a+2c+ 6e, b+3d+ 9f) which is NOT the same as (a+2c+2u, b+3d+3f).

Okay, here you did exactly that.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)

Yes. In fact, sinceSo it's not a vector space. Is this correct ??allproperties have to be true you really only needed to show that .