Suppose that R³ is given the norm ||(x, y, z) || = |x|+|y| + |2| and let S = {(x, y, z) = R³: 2x + y - 3z = 0}. Define a functional f on S by f(x, y, z) = x - z. (b) Determine ||f||.

Q: (a) Prove that f is a one-to-one correspondence. (b) Prove that ray AF is between rays AB and AE if…

A: (a) To prove that f is a one-to-one correspondence, we need to show that f is both injective and…

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Q: -2y 2x (x²+y²) ²³ (x²+y²)² Compute fF.dr, where F(x, y) = oriented counterclockwise. (Use symbolic…

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Q: Suppose A is a function that assigns to each subset of the plane a number in such a way that the…

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Q: Let S = Þ (D), where D = {(u, v) : u² + v² ≤ 1, u ≥ 0, v ≥ 0} and Þ (u, v) = (2u+1, uv, 3u + v). (a)…

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Q: Suppose F(x, y, z) = (ex, 2³, y² + 2) (a.) calculate V x F (b.) let C be the line segment from (0,…

A: (a.) To find: .(b.) To find: , where C is the line segment from (0, 0, 0) to (1, 2, 3).

Q: Consider F and C below. F(x, y, z) = yzexZi + e²j + xye*²k, C: r(t) = (2 + 4)i + (t² – 1)j + (t² -…

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Q: 3. Let C[0, 1] be equipped with the inner product (f, g) = f f(x) g(x) dx, where f = f(x) and g =…

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Q: 3. Let V denote the vector space of all functions f: R" → R, equipped with addition + : V x V → V…

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Q: sup norm

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Q: ) For the vector space C[0,1], define the inner product (f,g) = , f(x)g(x)dx. Let f = x + 1 and g =…

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Q: Exercise 3 Consider the subset W = {P(x) € P2 | P(4) = P'(2) = 0} of the space of quadratic…

A: W={P(x)∈P2| P(4)=P'(2)=0}Where P2={a+bx+cx2| a, b, c∈ℝ}(a) To find: a, b∈ℝ such that a+bx is in WLet…

Q: At what points (x,y,z) in space are the functions continuous? a. h(x,y,z)= In (2³-4x³ - 3y³ - 2) 1…

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Q: Let V be the vector space of polynomials in a over R of degree <3 and define an inner product f. g =…

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