# Condition for a set V to be a subset of a set X

• Oct 10th 2010, 09:50 AM
leftfootwonder7
Condition for a set V to be a subset of a set X
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.
• Oct 10th 2010, 10:17 AM
Jhevon
Quote:

Originally Posted by leftfootwonder7
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.