Question

Define W =  x y  : xy ≥ 0  . Decide if V is a vector space or notand prove your claim. (Hint: V is the union of the first and third quadrants in the xyplane)

Answer 1

$\left( 1,2 \right) ,\left( -2,-1 \right) \in V\\\left( 1,2 \right) +\left( -2,-1 \right) =\left( -1,1 \right) \notin V\\Not\,\,a\,\,vector\,\,space$