need some help
pic related is a linear algebra question im kinda stuck on. i have to verify that the union of the second and fourth quadrants of the cartesian plane, or the formation law on the right, is a vector space with the operations defined below.
thing is, if x*y <= 0, then say, (-8,0) belongs to the set, as does (7,-1), but then the sum of these two as defined would result in (-1,-1), which does not belong to the set. am i missing something here?
further, how do i go about proving the 8 conditions for the vector space? as in, representing a generic vector under the formation law conditions?
i need to finish this and 12 other exercises by midnight, so i am getting a little desperate.
if theres something unclear just ask me and i can elaborate, thanks in advance