document.write( "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. \n" ); document.write( "

Algebra.Com's Answer #642147 by robertb(5830) $\"\"$ $\"About$

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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.\r
\n" ); document.write( "\n" ); document.write( "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).\r
\n" ); document.write( "\n" ); document.write( "Thus, W is a subspace of V. \n" ); document.write( "

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