Consider inner-product = | f(x) g(x) dx defined for vector space C[-1, 1] , then for the function f(x) = 3 x the inner-product equals: Select one: О а.6 O b. 3 О с. 1 O d. zero

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Q: What is the dimension of the vector space M,x3R)?

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

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Q: 3. Prove that if r, y E RP, then ||r + yl|2 = ||x||2 + |ly||² holds if and only if r y = 0. 4. Prove…

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Q: Let V be the subspace of the vector space of all real-valued functions that is spanned by the setS…

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Q: Find the divergence of the vector field. F(x, y, z)= 6x¹0i-10xy ¹0j O divF(x, y, z) = 60x⁹-100xy⁹ O…

A: To find the divergence of the given vector field.

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Q: What is the dimension of the vector space S=abc detEM2x3(R): a=b=c=0}

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

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Q: Compute the vector assigned to the pointP = (−3, 5) by the vectorfield:(a) F(x, y) = (xy,y − x)(b)…

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

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Q: Let V be a vector space over R, and dimV=200. Let NEL(V) be a nilpotent operator such that null(N2)…

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

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Q: (b) Given vector fields F and G on R³, show that div(F x G) = Ğ · curl(F) – F - curl(C).

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Q: -dt. dF = (dr · V)F+ at

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Q: The function = ] f(x) g(x) dx defined for vector space C[-1, 1] satisfies : Select one: a.…

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Q: Show that whether the functions sint and cost in the vector space C[-n, 1]of continuous functions on…

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

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Q: Let X be the vector space of all or Can we obtain the norm defined on from an inner product?

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Q: 5. If a vector function F depends on both space coordinates (x, y, z) and time t, show that dF = (dr…

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Q: Verify Stoke's theorem for the vector field F = (2x - y) I– yz"J - y z K over the upper half surface…

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Q: ƏF dF = (dr. V)F+ -dt. at

A: Given: A vector function F depends on both space coordinates x, y, z and time t.  To Find:  To show…

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Q: Use the inner product 1 (f, 8) = f(x)g(x) dx in the vector space CO[0, 1] of continuous functions on…

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Q: Consider the vector space of continuous functions over the interval [-1,1] with the inner product…

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A: Given the function f:ℝn→ℝn. Given that, this function preserves the operation 'inner product'. Which…