Find the orthogonal projection of f onto g. Use the inner product in C[a, b] (f. g) = f(x)g(x) dx. C[-1, 1], f(x) = x, g(x) = 7 projf =

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A: Let F→x,y,z=zex-yezi→+2cosy-xezj→+ex-xyezk→ and C is the square with vertices…

Q: Which of the sets is orthoponal under the given inner product on C[O, T]? = S Puigenldx I. {1, sinx…

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Q: Find the potential function f for the field F. F= (4x3y10z10, 10x4y9z10 10x4y1029) O fix, y. 2) =…

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Q: The vector field F = ( , ,2²) has a scalar potential in the region R= {(r, y, z) E R³ : x> 0}

A: ANSWER: TRUE

Q: 3. Let f(x)=x² + 3 and g(x)=x³-1. Use the standard inner product on C[0, 1] to compute the…

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Q: Find the curl of the vector field F. F(x, y, z) = 4x² + 7y²j + 5x²k

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Q: Let E The orthogonal projection of y on H = span{ u 1, ú 2} is given by:

A: Given

Q: Let F = . a) Find a potential function for F, that is, a scalar field f(x,y) such that Vf = F. b)…

A: Given F=3x2y+y2+1,x3+2xy+2 a We have to find the potential function for F,that is a scalar field…

Q: Let f(x) = sin x and g(x) = sin x + cos x  in the vector space C, [0, 2π] with the inner product…

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

Q: Let f(x) = sin x and  g(x) = sin x + cos x  in the vector space C, [0, 2π] with the inner product…

A: Given that, f(x) = sin x and  g(x) = sin x + cos x Consider an inner product in them for f , g C ∈…

Q: Find the orthogonal projection of f onto g. Use the inner product in C[a, b] (f, 9) = (r, "rx…

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Q: Sketch the vector field F(x, y) = xi + yj and calculate the line integral of F along the line…

A: The solution are next step

Q: Use the inner product (f,9) = f(z)g(x) dz in the vector space C"0, 1] of continuous functions on the…

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…

Q: Find the gradient vector field (F(x, y, z)) of f(x, y, z) = In(4x + y + 62) . F(1, y, 2) =

A: we have to find the gradient vector field of f

Q: Show that the vector field F = 2xyi + (x² – 2 y)j is conservative and evaluate the line integral…

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Q: Find the divergence of the vector field F = < yx², xzª, zy³ div F =

A: f = y x2  ∂f/ ∂x = 2xy   g = x z4  ∂g/ ∂y = 0   h = z y3  ∂h/ ∂z = y3

Q: etch the vector field F(x, y) = xi + yj and calculate the line integral of F along the line segment…

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Q: Evaluate f(x²y+3xyz) dxdydz by applying the transformation u = x, v=xy and w=3z, where G is G region…

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Q: Sketch the vector field F(x, y) = xi + yj and calculate the line integral of F along the line…

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Q: Is = xjx + yjy+zźz3 an inner product on R'?

A: No it is not an inner product.  Inner product looks like a dot product.

Q: Find the divergence of the vector field F. F(x, y, 2) = In(9x+ 8y² )i + 72xyj + In(8y² + 5z? )k #6…

A: Solution is done in step 2 and 3

Q: Find the gradient vector field (F(r, Y, 2)) of f(x, y, z) = In(4x + 6y + 22) . F(7, y, 2) = (

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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: The projection of y onto i is a scalar multiple of y.

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Q: Find the null space of the linear transformation T: R →R TE, y, z) = (x + y, z). defined by

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Q: Find a potential function for the vector field F by inspection. F = (4x, 4y) Ф(х, у) 3

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Q: Determine a scalar s such that A2 x = sx when Ax = r x.

A: Given that Ax=rx. Multiply both sides of the above equation by A and simplify as follows.

Q: Show that the function does not define an inner product on R3, where u = (u1, u2, u3) and v = (v1,…

A: For satisfying the inner product condition, function has to follow these three conditions: 1)…

Q: Show that the vector field F = 2.xyi + (x – 2 y)j is conservative and evaluate the line integral %3D…

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Q: Show that the function defines an inner product on R3, where u = (u1, u2, u3) and v = (v1, v2, v3).…

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Q: Determine a scalar r such that Ax = rx, where 1 A = and X=

A: Given, A=2112, x=11

Q: Find the curl of the vectòr field F(x, y, z) = 2xyzi + 8yzj + 5zk

A: According to our guidelines we are supposed to do only one question.  Kindly repost other question…

Q: On a vector space W of all continuous functions from R to R, define I, : W → W as I,[f(t)]= J', f(t)…

A: Yes  given function is linear transformation

Q: Let H be the set of all points in the second quadrant in the plane V=R^2. That is, H={(x,y) | x ≤ 0,…

A: Here in the question H be the set of all points in the second quadrant in the plane V=R2. That is,…

Q: Show that V x VG = 0 for all scalar field G(x,y,z). %3D

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Q: Find the divergence of the vector field F. F(x, y, z) = In 5x²+ + 10xyj + In( 2y2 + 722)k div F(x,…

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Q: Use the inner product (f, 9) = f(-1)g(-1) + f(0)g(0) + f(1)g(1) in P, to find the orthogonal…

A: Vbb

Q: Find the orthogonal projection of f onto g. Use the inner product in C[a, b] (f, g) = f(x)g(x) dx.…

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Q: Show that the vector field F = 2xyi +(x² - 2y)j is conservative and evaluate the line integral (F•dš…

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Q: Consider the vector field F(x,y,z)=(−3x^2,8(x+y)^2,9(x+y+z)^2). Find the divergence and curl of FF.…

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Q: Find the orthogonal projection of f onto g. Use the inner product in C[a, b] (f₁ g) = f(x f(x)g(x)…

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Q: Find the orthogonal projection of f onto g. Use the inner product in C[a, b] (, 9) = [". f(x)g(x)…

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Q: a) Calculus f(x) = x, g(x) = e*, %3D (f, dx b) Let f(x) Example 5, 1 and g(x) = x be functions in…

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Q: Find the orthogonal projection of f onto g. Use the inner product in C[a, b] (f 9) = [" r« f(x)g(x)…

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Q: Find the orthogonal projection of f onto g. Use the inner product in Ca, b] (f, 9) = ["«x»9(x) dx.…

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

A: Given that,

Q: 1) Verify that d/dx(fg) is a vector space over R, or explain why it is not.

A: The objective is to find whether the ddxf.g is a vector space over ℝ. Since it is known that…

Q: Show that the function defines an inner product on R2, where u = (u1, u2) and v = (v1, v2). ⟨u, v⟩ =…

A: Given function u,v=u1v1+9u2v2 where u=u1,u2 and v=v1,v2 The function is defined on R2. To show that…

Q: (b) Perform the Gram-Schmidt orthogonalization process for u = x +1, u2 = x² + 3, u3 = Va using the…

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Q: Determine a scalar r such that Ax = rx, where

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