2. Let T: C² C³ be defined by T((x, y)) = (x,x+y,y) and S: C³ → C² be →> defined by S((x, y, z)) = (x-y, y-z). (a.) Compute (SoT)((x, y)) (b.) Determine whether SoT is linear.

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A:

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A: Please see the explanation below

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A: Find

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A:

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A:

Q: 29. Consider the function f: R² →R: (x,y) → f(x,y) = g( Determine the gradient of f. 1 1 2x - 2y g(1…

A: Please check the next step for details.

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A:

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A: Note: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts…

Q: Consider (x, y, z) = 10xyz - 4x²y³ G(x, y, z) = Gx(x, y, z)i + Gy(x, y, z)] + G₂(x, y, z) k and…

A: Page 1 Page 2 Page 3

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A:

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A: If p(x, y) = (y+2, 2-x) and u(x, y) = (x, -y), find the formula p∘p∘p∘u and use it to determine its…

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A:

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A: We are given Non homogeneous differential equation. We have to find their solution.

Q: 20.- From the following equation T: R 2→ R 2 determine, AND SHOW IF T IS LINEAR T(x, y) (2x+y,x - y)…

A:

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A: The given function  is given by .To show that T is linear.