V = F(R, R), the vector space of all real valued functions f(x) of a real variable x. Which are subspaces of V?(adsbygoogle = window.adsbygoogle || []).push({});

(A) {f | f(0) = 0}

(B) {f | f(0) = 1}

(C) {f | f(0) = f(1)}

(D) [itex]C^0(R)[/itex] = {f | f is continous}

(E) [itex]C^1(R)[/itex] = {f | f is differentiable and f' is continous}

(F) P = {f | f is a polynomial}

(G) [itex]P_d\,\,\,\,=\,\,\,\,{f\,\in\,P\,|\,deg(f)\,\le\,d}[/itex]

(H) [itex]{f\,\in\,C^1(R)\,|\,f'\,=\,f}[/itex]

I have no idea what the last five of these instances mean. Case (C) is not a subspace because it only satifies the first rule that the set {0} be in the space before it can be considered a subspace, right?

Please help, I don't understand the terminology of the last five examples!

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# Homework Help: LINEAR_ALGEBRA: What is a subspace of V = F(R, R), the vector space of all real funcs

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