SOLUTION: let V = F be the vector space of all real-valued functions and Let W = {f ∈ F : f(0) = f(1)}. Show that W is a subspace of V.

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Question 1026858: let V = F be the vector space of all real-valued functions and Let W = {f ∈ F : f(0) = f(1)}. Show that W is a subspace of V.
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
We can use the subspace criterion: The subset W is a subspace of V if for any f(x), g(x) in W then every linear combination c%5B1%5Df%28x%29%2Bc%5B2%5Dg%28X%29 would also be in W.
This is almost automatic, clearly c%5B1%5Df%280%29%2Bc%5B2%5Dg%280%29+=+c%5B1%5Df%281%29%2Bc%5B2%5Dg%281%29 since f(0) = f(1) and g(0) = g(1).
Thus, W is a subspace of V.