1. Let V = C[-2,2], the vector space of continuous functions on the closed interval [-2, 2]. Let f, g € V and define the inner product of f and g to be (f, g) = | f(x)g(x) dx. Let h(x) = x² and let k(x) = 7x*, compute (h, k). Simplify your answer completely.

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Q: 1 Let S=(x | x=a +b +d 1 +c 1 1 where a,b,c,dER. Show explicitly that S is a vector space.

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A: Given set is  V={(x,y):x=>0 }

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Q: 7. Let C[-7,7] be the vector space of continuous function over [-n, 1] with an inner product 1 (5,9)…

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A: The given functions are, In the vector space,

Q: Find the boundary of the sequence xn in the normalized vector space C [a, b], if it exists. 4 cos 3…

A: The given sequence is: xnt=4cosn3t5+cosnt a=-5π, b=-4π

Q: Let V ((x,y): x 20) with standard operation on R2. Is V a vector space?

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A: It is given that fx=-5x2-3 and gx=9x-7. We have to evaluate f, g, f, g and αf, g where αf, g is the…

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Q: Find the boundary of the sequence xn in the normalized vector space C [a, b], if it exists. 4 cos/3…

A: Solution: Here the sequence is xnt=4cosn3t5+cosnt and a=-5π,  b=-4π

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Q: 1. Let V = C[-2, 2], the vector space of continuous functions on the closed interval [-2, 2). Let f,…

A: We can just multiply h and k and integrate  Then after simplifying we are getting answer

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Q: Let V = {(x, y): x 20} with standard operation on R2. Is V a vector space?

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A: Given F=8x2+y2, x2+y252, xyz17 is a vector field on U=x, y, z∈ℝ3 | x, y≠0, 0 We will find its curl…

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Q: Consider inner-product = | f(x) g(x) dx defined for vector space C[-1, 1] , then for the function…

A: The solution is given as

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Q: a) T: M, → R, where M, is the vector space of n by n matrices over a field, and T (A) = det(A). b)…

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Q: Sketch the space curve. Vector-Valued Function r(t) = -ti + 2tj + 3tk O 5 5 5 k k 2 -2 5 Z 2…

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A: To show that any additive function between the vector spaces is linear transformation.

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Confidence Intervals

When we calculate intervals in probability and statistics, it can be simply termed as finding out a confidence interval. The confidence interval is usually calculated from the data set which is observed. The value of the parameter that needs to be calculated is present here only.