Questions tagged 'Vector Space'

consider v={(x,y) :xy=0 } with the usual vector addition and scalar multiplication in R^2 is (v,+,.) a vector space?

Consider the set ( V = {(x, y) \in \mathbb{R}^2 : xy = 0} ) along with the usual vector addition and scalar multiplication defined in ( \mathbb{R}^2 ). Is the pair ( (V, +, \cdot) ) a vector space?