# Subset of Vector space

• Apr 11th 2011, 09:23 PM
Subset of Vector space
W = {a + t^2, aER}; V = P2

So bascially what I need to do is to determine if a + t^2 is a subspace of P2 but I'm not too sure on how to do it. In lectures we learnt subspaces using vectors where we had to determine using the zero vector then check if it is closed under addition and Scalar multiplication but I don't know how to do it when it relates to a polynomial so I hope someone can just give me a few pointers
• Apr 11th 2011, 09:27 PM
mr fantastic
Quote:

W = {a + t^2, aER}; V = P2

So bascially what I need to do is to determine if a + t^2 is a subspace of P2 but I'm not too sure on how to do it. In lectures we learnt subspaces using vectors where we had to determine using the zero vector then check if it is closed under addition and Scalar multiplication but I don't know how to do it when it relates to a polynomial so I hope someone can just give me a few pointers

Apply the Subspace Theorem.
• Apr 11th 2011, 09:57 PM
Deveno
is the 0-polynomial: 0 + 0t + 0t^2 in W?

if no, then stop. if yes, then continue:

for a + t^2, and b + t^2 in W, is (a + t^2) + (b + t^2) in W?

if no, then stop. if yes continue:

for a + t^2 in W, and c in R, is c(a + t^2) in W?

if no, then stop. if yes, W is a subspace of P2.