Suppose a change of coordinates T: R → R* from the uv-plane to the sy-plane is given by * = -3v – 4u + 2, y = 2 – 5u – 4v. a) Find the absolute value of the determinant of the Jacobian for this change of coordinates. | 8(2, y)| = |det | a(4, v)| b) If a region D* in the u-plane has area 7.49, find the area of the region T(D*) in the zy-plane. Area =

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A: Statement (S1) proves that  I2 , A, A2  are linearly dependent.

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A: Note: Since we only answer up to 3 sub-parts, we'll answer the first 3. Please resubmit the question…

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A: To solve this problem we use chain rule.

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A: To find the divergence of the given vector field.

Q: Exercise 3.6. Prove that a linear order is antisymmetric: V different x, y E X,-(x < y Ay < x).

A: Note: Since you have asked multiple questions, we will solve the first question for you. If you want…

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A: Given that,

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A: Follow the procedure given below.

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Q: Let f: C → C be differentiable at zo. Considering ƒ as a map R? → R², prove that f'(zo) = kR where k…

A: (a)

Q: (1) Determine the Jacobian ôx/ôq for the following system: x= [u, v, w], q = [x, y, AJ. u = x + 3y…

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 4 Let y = U2 = -7 U1 = -4 4 -6 -2 -9 Compute the distance d from y to the plane in IR° spanned by u̟…

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Q: (b) Perform the Gram-Schmidt orthogonalization process for u = x +1, u2 = x? + 3, u3 Va using the…

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A: We have find the jacobian

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A: true please see explanation in step 2

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A: The Wronskian is, 9cx + 18ac ln(bx)  The solution is as follows :

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A: (a)

Q: 1. Let R? have the inner product of Example 1, and let x = (1, 1) and y = (5, – 1). a. Find ||x||,…

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Q: -52 +1 -3 If zo =-1, G(z) = and f (y) = -5 y1 4 - 2 y2 Y3 + v -4 y1 - 2 32, find the Jacobian of G…

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Q: Let f: C → C be differentiable at zo. Considering f as a map R? → R², that f'(zo) = kR where k is a…

A: (a)

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Q: 5. Given that G(x, y) = (x² + 1, y²) and F(u, v) = (u + v, v²), compute the Jacobian derivative…

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