Did I do this question right?

[mahjk17]

The question states, "Show that the positive quadrant Q = { (x,y) ∣ x,y > 0} ⊂ ℝ^2 forms a vector space if we define addition by (x(1),y(1))+(x(2),y(2))=(x(1)x(2),y(1)y(2)) and scalar multiplication by c (x,y)= (x^c,y^c)."
My attempt: x,y are ordered pairs, it follows that x(1),y(1)=x(2)y(2) if and only if x(1)=x(2) and y(1)=y(2) since x and y are vector space then the set Q will remain positive.
Am I on the right track or am I completely off?

 

[daon2]

Aren't there 10 or so axioms you need to verify?

I'm not sure what you have written down there, but it looks like you are attempting closure under addition.

If (a,b), (c,d) belong to the set, then a,b,c,d > 0. Therefore, a*c > 0 and b*d >0. So (ac,bd) is also in the set.

 

[mahjk17]

Wow, its so simple but I make way too complicated. I am going to do a lot more practice problems on it! Thanks again Daon2!!