4. Let the vector space P([-1,1]) have the inner product = f(t)g(t)dt, using 21

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A: For vector field FF and scalor field g we have to solve a), b), c).

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A: We will write  as a linear combination of the vectors

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A: Here we have to find the given definite integral.

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A: “Since you have posted multiple questions, we will provide the solution only to the first question…

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A: Definition used .

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A: We use the process of mathematical induction

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A: solution.This is an optimization problem with 4 variables and 2 constraints. We can introduce slack…

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A: Note: As per the guidelines, we are supposed to answer only 3 subparts. Please repost the other…

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A: We shall be using the fact that a^p-1 =1 mod p

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Q: 2. Let n₁,..., nk be pairwise relatively prime positive integers, and let n = n₁ ... nk. Recall we…

A: this is also famous known as the chinese remainder theorem

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Q: Use Theorem 7.4.1. THEOREM 7.4.1 Derivatives of Transforms If F(s) = L{f(t)} and n = 1, 2, 3, . . .…

A: Note that : Since you have posted multiple questions, we will provide the solution only to the first…