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Let S be a nonempty set and F a. field. Prove that for any SQ S, {/ T(S, F): /(s 0 ) =

Chapter 1, Problem 13

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QUESTION:

Let S be a nonempty set and F a. field. Prove that for any SQ S, {/ T(S, F): /(s 0 ) = 0}, is a subspace of F(S, F).

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QUESTION:

Let S be a nonempty set and F a. field. Prove that for any SQ S, {/ T(S, F): /(s 0 ) = 0}, is a subspace of F(S, F).

ANSWER:

Step 1 of 2

Let be a nonempty set and be a field.

To prove that for any , is a subspace of .

Let us consider

Clearly,

If we consider the zero function, the for any , .

Therefore, is a nonempty subset of .

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