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6. Let ƒ : R² → R² be a differentiable function. Suppose that f(x, y) = (u(x, y), v(x, y)), the Jacobian matrix is given by Ju ?х Əv ?х Jf(x, y) = Ju dy Əv , y) (x, y) Əy Uz(x, y) Uy (x, y) Vr(x, y vy(x, y)), In the following given f, find u(x, y); v(x, y) and the corresponding Jacobian matrix. (a) f(x, y) = (x + 2y,3x −y) (b) f(x, y) = (4x + y, sin x) (c) f(x, y) = (ln(1 + x² + y²), sin x) (x, y) (x,y)

6. Let ƒ : R² → R² be a differentiable function. Suppose that f(x, y) = (u(x, y), v(x, y)), the Jacobian matrix is given by Ju ?х Əv ?х Jf(x, y) = Ju dy Əv , y) (x, y) Əy Uz(x, y) Uy (x, y) Vr(x, y vy(x, y)), In the following given f, find u(x, y); v(x, y) and the corresponding Jacobian matrix. (a) f(x, y) = (x + 2y,3x −y) (b) f(x, y) = (4x + y, sin x) (c) f(x, y) = (ln(1 + x² + y²), sin x) (x, y) (x,y)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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6. Let ƒ : R² → R² be a differentiable function. Suppose that f(x, y) = (u(x, y), v(x, y)), the Jacobian matrix is given by J₁(x, y) = (u₂(x, y) u₂(x, y)) Vr(x, y vy(x, y)), In the following given f, find u(x, y); v(x, y) and the corresponding Jacobian matrix. (a) f(x, y) = (x + 2y,3x −y) (b) f(x, y) = (4x + y, sin x) (c) f(x, y) = (ln(1 + x² + y²), sin x) Ju ?х Əv ?х Ju Əy Əv , y) (x, y) Əy (x, y) (x,y)
Transcribed Image Text:6. Let ƒ : R² → R² be a differentiable function. Suppose that f(x, y) = (u(x, y), v(x, y)), the Jacobian matrix is given by J₁(x, y) = (u₂(x, y) u₂(x, y)) Vr(x, y vy(x, y)), In the following given f, find u(x, y); v(x, y) and the corresponding Jacobian matrix. (a) f(x, y) = (x + 2y,3x −y) (b) f(x, y) = (4x + y, sin x) (c) f(x, y) = (ln(1 + x² + y²), sin x) Ju ?х Əv ?х Ju Əy Əv , y) (x, y) Əy (x, y) (x,y)
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