remember, we say P is a necessary condition for Q if Q => P. So that is what you need to show.
if V is a subspace of X, then the aforementioned condition holds.
Prove that a necessary condtion for V to be a subspace of a k-vector space X is that:
ax + by is an element of V
for a,b elements of k and x,y elements of V.
Im not sure what im being asked to prove here. I know that the condition is one of the axioms needed for a set to be a vector space. Basically im looking for help on what the question is asking.
remember, we say P is a necessary condition for Q if Q => P. So that is what you need to show.
if V is a subspace of X, then the aforementioned condition holds.