Let Dg = { x, y | x2=1, y3=1, xyx = y} consider the map p: D3 → GL₂ (A) defined by p (y) = P(-(i) p (x) = 1 cos 2/3 -sin 2/3 sin 2/3 cos 2/3 Check that p is a representation. (i) (ii) Find the character of p.

Q: Let X {1,2, 3} and Y {3,4}. Define f : X → Y as follows: = f(2) = 3 and f(3) = 4. Draw an arrow…

A: We will draw the arrow diagram for function mapping from set A to set B.

Q: Find all harmonic conjugates of u(x, y) = x³ - 3xy² + 2y.

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Q: Sketch a contour map for f(z. y) using the k-values, k = 1, 2, 3. |f(x, y) = |x| + sin(y)

A: Given : f(x,y)=|x|+sin(y)   To sketch : contour using the k-values k=1,2,3

Q: F. dr Evaluate So

A: In this question, we have to evaluate the line integral for given vector function along the given…

Q: Let F = cos(4t) i + 3tj+ 4t°k and G = t cos(4t) i + t j+4e#k Find the cross product F x G =

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Q: Write the function f(z) = z + 1/z in the form f(z) = u(r, theta) + iv(r, theta) (Answer is f(z) = (r…

A: f(z)=(r+r1​)cosθ+i(r−r1​)sinθ   Explanation:

Q: (a) Show conclusively that the map f : R² → R defined by f(x, y) = x cos(y) is not linear.

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Q: *) Use the Wronskian to determine whether the functions y₁ = sin(3x) and y₂ = cos(4x) cos(4x) are…

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Q: Z=x+y+ cos(x+y)

A: Given,        z=x+y+cos(x+y)

Q: Evaluate ∫ ▽f*dr Where f(x,y,z)=cos(πx)+sin(πy)-xyz and C is any path that starts at (1,1/2,2) and…

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Q: Find the adjoint of F:C3 tends to C3 defined by F(z1, z2, z3)=(2z1+(1-i)z2 , (3+2i)z1 -4iz3 ,…

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Q: Evaluate F.dr where F(x, v)=xyi (4, 0).

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Q: A. Verify Clairaut's Theorem for the given function: F(U,W) = Sin(UW)- 4U?w2 %3!

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Q: If v(r, y) is a harmonic conjugate of a harmonic function u(x, y) show that the function g(r, y) =…

A: Harmonic function: A two variable function ux, y is said to be harmonic, if the function is twice…

Q: show that the function 3x²y-y³ ty is he harmonic and then find it's Harmonic conjugate v (x, y)

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Q: Find and sketch the domain of the function f(x,y) = cosx + V3x-y+2

A: The given function is .The objective is to find the domain of the function and sketch the domain.

Q: CD has coordinates C(-8,-2) and D(-4,-12). determine the coordiantes of C'D' if (x,y) -> (1/2x,1/2y)…

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Q: (4) Let f₂ = df/az and ƒz = df/az. Recall ƒ = u + iv, the notation f is used for the complex…

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Q: 4) Let ƒz = dƒ/əz and ƒz = 0ƒ/əz. Recall ƒ = u + iv, the notation f is used for the complex…

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Q: Show that the function u = In(X² + Y2) is harmonic and find the conjugate harmonic v.

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Q: Let f is used for the complex conjugate function u – iv. Verify the chain rule (fog)z = af/az and fz…

A: Bartleby Guidelines:-“Since you have posted multiple questions, we will provide the solution only to…

Q: Define to mapping pi : R2(arrow)R by pi((x,y)) = x. Find the kernel of pi.

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Q: 1. (a) Find the domain and range of f. (b) Draw a contour map of f for k=-1,0,1. (c) Sketch the…

A: (a) For the given function, f(x,y)=y+x+2, Assume f(x,y)=z; Here,  z=y+x+2 The domain of z has all…

Q: Consider the function f: N× N → Q given by f(x, y) = your claim. X y + 1 Find the image of f and…

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Q: What is the mapping notation for y = -4 sin(x + 3) − 8? (a

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