be an Given f: R³ → R, explain the relation between the following sets: {(x, y, 2) E R³: f(x, y, z) = c} {(x, y, z) e R³: (foT)(x, y, z) =c} transformation

Q: Describe the translation for ABC A'B'C'. y A' A C' B' C 3.

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Q: Show that the operator U is a partial isometry U: L² ([0,1]) → L² ([0,1]), Uƒ(x) = X[0,1] ƒ(x)

A: To show that the operator U:L2([0,1])×[0,1]→L2([0,1]) defined by Uf(x)=χ[0,1](x)⋅f(x) is a partial…

Q: Use Stoke's Theorem to evaluate Į F· dr where F (x, y, =) = , and C is the triangle with C vertices…

A: given Fx,y,z=z2,y2,xy ⇒Fx,y,z=z2i^+y2j^+xyk^ and a traingle C with vertices 1,0,0 ,0,1,0 ,0,0,2 to…

Q: Let R be the relation on R given by R= {(x, y) : xy > 0}. Is R reflexive? symmetric? antisymmetric?…

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Q: 11) Let f: IR4 → IR³ be defined by : IV f(x₁y₁z₁t) = (2x+y-t, x+8y-92- 2t, x-2y + 3z) (a) show that…

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Q: Let T: R3 -> R2 be defined by T(a, b, c) = (a + b, 2a —- c). DescribeT-1(1, 11).

A: T: R3 -> R2 Hence, T-1 : R2 ----> R3 So, necessarily we have to find a, b & c such that…

Q: 2) The contour map of f(x, y) is shown below. Use it to find fx (1,3) 10 10 8 8 6 =2 6 0 x=2 6 8 10

A: fx​(1,3)=1   Explanation:From the given contour map, we can see that, f(1,3)=4  Similarly we can…

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: Here are some transformation rules. For each rule, describe whether the transformation is a rigid…

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Q: If y and z are functions of u and v, then the Jacobian of the function transforming (x, Y, z) → (x,…

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Q: (-1,2, 3).

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