The question:

Show that the set

with the usual rules for addition and multiplication by a scalar in is not a vector space by showing that at least one of the vector-space axioms is not satisfied. Give a geometric interpretation of this result.

My attempt:

There's no solution to this answer in my text. My understanding is that this set is not closed under scalar multiplication, since multiplying by -1 will reverse the conditions on and . Is this correct?

As for the second part of the question, it asks for a geometric interpretation, which I'm not sure about. It's a 3D object, but otherwise I don't know how else to interpret it. Any ideas?

Thanks.