2. Let n e N and suppose X is a set with n elements. Define V as the set of all functions f: X C. The set V together operations + and· described below (f + g)(x) = f(x) + g(x) Vx E X, (c. f)(x) = c· f(x) Vc E C and Vx € X forms a vector space (don't verify this anymore). Find a basis of the vector space V.

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A: We want g o h = f.     So, we want g o h(1) = f(1) = 7            and g o h(3) = f(3) = 7   Now,…

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A: Note: As per our guidelines, we can answer the first question. Please repost the remaining…

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Q: Can you show an example of Null space?

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A: No, we can write it.

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A: Dear student, as per our guidelines we can answer only first three subqustions. So kindly resubmit…

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