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) (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 would also be in W.
This is almost automatic, clearly since f(0) = f(1) and g(0) = g(1).
Thus, W is a subspace of V.
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