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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(choose chapter or problem)
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).
Questions & Answers
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 .