Let -? and ? denote two distinct objects, neither of which is in R. Define an addition and scalar multiplication on R U {?} U {-?} as you could guess from the notation. Specifically, the sum and product of two real numbers is as usual, and for t ? R define

t? = { -? if t<0 , 0 if t=0, ? if t>0

t(-?) = { ? if t<0, 0 if t=0, -? if t>0

t+? = ?+t=?, t+(-?)=(-?)+t=-?, ?+?=?, (-?)+(-?)=-?, ?+(-?)=0

IsR U {?} U {-?} a vector space over R? Please Explain.