c) Is W = {(x, y): y = 2x} a subspace of R2 ? Explain your answer. 1

Q: Find the curl of the vector field at the given point. F(x, y, z) = x²zi – 2xzj + yzk; (7, –9, 5)

A: Given vector field F(x,y,z) =x2 z i -2xz j +yz k   ; (7 , -9 , 5)

Q: Compute fx + fxy + fyyzz, where f(x, y, z) = z sin(xy)

A: Given f(x,y,z)= z sin(xy)

Q: Find llFll and sketch several representative vectors in the vector field.

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

A: A vector space is a set V that satisfies the following 8 conditions. Here two operations "+" and "."…

Q: Find all points (a, b, c) on the sphere x2 + y2 + z2 = R2 where the vector field F = yz2i + xz2j +…

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Q: Find the gradient vector field of f(x, y, z) = 9x² + 8y* + 6z3

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Q: Find the flux of the vector fielol F from the baunelries of the given region (o). 37 2. (D): solid…

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Q: Find the curl of the vector field at the given point. F(x, y, z) = x2zi – 2xzj + yzk; (9, -9, 5)

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Q: V=(x^2)yi-xyj+xyzk

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Q: Match the vector field with its graph. F(x, y) = yi 1 |||||||||| 三 6 靈

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Q: Find the gradient vector field of f(x, y) ,3

A: Given,          The gradient vector field of fx,y=x6y3.

Q: Find the flux of the vector field F = (y, – z, x) - 2, - across the part of the plane z = 2 + 3x +…

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Q: of the valve matix is consistant e an linear

A: Given augmented matrix is: -412h2-6-3 Let the variables be x, y. The above augmented matrix will…

Q: Sketch a few representative vectors of vector field F = ⟨0, 1⟩along the line y = 2.

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Q: Find the gradient vector field of f(x, y, z) = x³y* + y° z³ + xz°.

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Q: find laplace of f(x,y,z)=2x3y2z2

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Q: he upward flux of

A: Introduction: Let F be a function and let the region is S, then the flux of the function is given…

Q: Find the gradient vector field Vf of f. 1 f(r, y) = (y – 2)?

A: For a given vector fx, y the gradient vector denoted by ∇f is ∂ ∂ xf∂ ∂ yfSo,=∂ ∂ x12y-x2∂ ∂…

Q: Find the gradient vector field of f(x, y, z) 5x+ 2y+8z

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Q: dz - Prove that : Iz%3D2 %3D z%3D2 z+1 2in.

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Q: Find the divergence of the vector field. V(x, y, z) = 4yzi + 6xzj + xyk div(V) =

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Q: Bounded by the cylinders z = 2x2, y = x² and the planes z = 0, y = 4

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Q: Find over xlapping area two equatione also gemetrical nepresentahon 2. 4'+v?=n, u?+cV- vn)=1 whore n…

A: Given curves are,…

Q: Let xbe inner Product and ||x1|=|ly|| = 1 x+y Lix.y ? why?

A: Given that X is an real inner product space. x ,y be two unit vector from X then need to show that…

Q: Integrate counterclockwise z + 6 dz, C: |z – 1|= 4 Z – 2 z + 6 dz 2 ||

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Q: Find the curl of the vector field at the given point. F(x, y, z) = x²zi – 2xzj + yzk; (9, -9, 9)

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Q: Vector Field F = 6xi + (2y – y²)j+(6z – x³)k is Conservative Select one: True False

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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: Is the vector field F = [yze"yz, xze#yz, xye"yz] conservative? %3D O Yes O No

A: The vector field is conservative if ∇×F→=0 therefore, find ∇×F→ ∇×F→=ijk∂∂x∂∂y∂∂zyzexyzxzexyzxyexyz

Q: f(x,y) = 2x3+4y3-3x2-120x-192y+5 Is f(x,y) a curve, vector field, or surface?

A: To check whether it is a curve, vector or surface. f(x,y) = 2x3+4y3-3x2-120x-192y+5

Q: Find the divergence of the vector field. V(x, y, z) = 7e*Yj – 9e*Yj + 8EY²K - div(V) II

A: A detailed solution is given below.

Q: Integrate f(x,y,z) = x-3y + z over the line segment joining the points (0,0,0) and (2,2,2). %3D

A: Here, we need to integrate f(x, y, z)=x-3y2+z over the line segment joining the points (0, 0, 0) to…

Q: Find the gradient vector field of flx, y, z)=x'y+y%z4+xz6 O V flx, y,z)= (3x?y+z°, 5x³y³ + 4y*zA,…

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Q: 4. Show that ||y|| = maxxela.b]ly'(x)| defines a norm for the linear space Y - %3D {y e C' [a, b]: (…

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Q: The solid bounded by z = x, z = 2 – x², z + y = 3, and y = 0

A: Volume of a solid is obtained using triple integration by the formulae =∫∫∫dx dy dz The solid is…

Q: Find the kernel of linear map L:R R given by L(x,y,z)%3D(0,z,y)?

A: There is no such introduction for the solution.I have explained it within the solution.Please go…

Q: Compute the gradient field of f(x, y, z)= e^z + xy^2

A: Take gradient to solve

Q: Consider the set S = yl E R : 4x +6z=7y, x – 13y=0 . Is this a subspace of R ? Explain why or why…

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Q: xi + yj F(x, y) = k- x² + y2'

A:

Q: Find the curl of the vector field at the given point. F(x, y, z) = x²zi – 2xzj + yzk; (9, -9, 7)

A: The curl of a vector field F is defined as  ∇×F=i^j^k^∂∂x∂∂y∂∂zf1f2f3

Q: d.x = -2x + 5Y dt dy -2.x + 4y dt 5 cost X = \ sin t et 3 cost –

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Q: Find the gradient vector field of f(x, y) = In(2x + 3y) V

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Q: Calculate F=, around the triangle with vertices: (0,0,2), (2,0,0) and (0,2,0). Can you use Stoke's…

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Q: $ ((x,y) (E,6) )e product Prove 2 xt + 3yt on e?. Gompute inner IL(,2), where the norm i's…

A: We have to prove that f( (x, y) , (t, t) ) = 2xt + 3yt is an inner product on R2 . 1.) < ( 0, 0 )…

Q: Af V s vector space th cV = V

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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: Find the curl of the vector field at the given point. F(x, y, z) = x²zi - 2xzj+yzk; (9,-9, 9) curl F…

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