Let T: R-R° be a linear operator given by T(x, y, z) = (x+y, x-y, 0) which of the following vector is in Ker T: O (2, 2, 0) None O (0, 2, 0) O (2, 0, 0)

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)

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Q: Let r1(t) and r2(t) be continuous vector functions with two components, and let t0 be a point in the…

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Q: Let V be a vector space, T a linear operator on V, and v, w E V. Suppose that T(v + w) = v – 2w and…

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Q: Find the curl of the vector field F(x, y, z) = e" sin yi – e" cos yj O -2e" cos yk O -2e" cos y O…

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Q: Find the curl of the vector field F. F(x, y, z) = (2y - z)i + e²j + xyzk

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Q: If (a, b) is a local maximum of f, then D, f(a, b) = 0 for any unit vector u e R?. True False

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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 r(t) =[x(t), y(t), z(t)]. Provide a definition for the continuityof the vector function r at a…

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Q: Find the curl of the vector field F. F(x, y, x) = 2yz'i + 3xj +&xk O 15r4 O 15:3 O (8yz – 8]j +…

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Q: Give an example of a rigid motion T in C n, T(0) = 0, which is not a linear transformation.

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Q: Integrate the vector field h (x, y, =) = xy i +yz j+ xz k over r (1) =ui+ử j+ư k, u E[-1,1]. a) 0 b)…

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Q: Two vector fields are F = -10 ax + 20 x (y–1) ay and G = x y ax – 4 ay + z az. For the point P(2,…

A: Given vector fields are F=-10 ax +20 xy-1 ayG=2xy ax -4ay +z azPoint P =2, -3, -4

Q: For F(x, y, z) = y²z³ i + 2xyz³ j + 3xy²z² k, determine whether or not the vector If it is…

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Q: Match the vector field to its graph. 1. 2. = %3D 3. F (x, y) 1 = F (x, y) = F (x, y) 4. E 5.

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Q: Let U ⊂ Rn be open and f : U → Rm be differentiable at a ∈ U. Prove that for any vector ~v ∈ Rn,…

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

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Q: Let o = 2 In(r), where r= V x2 + y2. Express Vo in terms of the unit radial vector e, in R2. tep 1…

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Q: Compute the curl, V x F, of the vector field. F(x, y, z) = 7xi + 9yj + 2zk curl(F) = -7xi – 5yj +…

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Q: Let F = (4t + 2, sin(2t), 4r“) Find the indefinite vector integral F(t) dt = ( |) + (c,,C2, Cs)…

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Q: (E) x + y T z + 3 Check that T is not linear by finding two vectors u, v which violate the additive…

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Q: Let, T:R' → R;T(x, y, z) = (x + y+ z,2y + z,2 y+3z) verify that [T][v]s = [T (v)]; for any vector v…

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Q: Find a function f (x, y, z) such that ∇f is the constant vector〈1, 3, 1〉.

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

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Q: Consider the vector field i = P(x, y) = –3y+ ¤(x² + y² – 1), ý = Q(x, y) = 3x +y(x² + y² – 1) | %3D

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Q: Find the curl of the vector field at the given point. F(x, y, z) = x²zi – 2xzj + yzk; (3, -9, 7)…

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Q: x – y T x + Y. a) A vector in im(T) that is not 0 is

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Q: The vector field F(r, y) = (2xy +y) dx + (æ + 2xy) dy is conservative. %3D The function f(x, y) = x²…

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Q: Let V be a finite-dimensional inner product space over C and let u, w€ V be fixed non-zero vectors…

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Q: Consider the vector field F(x, y, z) = (-2y, –2x, 8z). Show that F is a gradient vector field F = VV…

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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) curl F…

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