So my first thought is we would have to check for both cases (x1,x1) and (-x1,-x1)
βa=(βx1,βx1)T for the case where a<0 βa(-βx1,-βx1)T
thus it is closed under scalar multiplication.
a+b=(x1+v1,x1+v1) for the case where a and b<0 [-(x1+v1,x1+v1)]T
thus closed under addition.
I would think this would be a subset, however the book says this is false. Where did I go wrong?