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In Exercises 27–32, functions x = x(u, v) and y = y(u, v) are given that determine transformations from an XY-coordinate system to a UV-coordinate system in R2. Use these functions to determine a region in the XY-plane that has the image specified for the given values of u and v, and find the Jacobian of the transformation.

x=u-vandy=u+vfor0u2and0v1

Short Answer

Expert verified

The Jacobian of transformation is equal to2.

Step by step solution

01

Given information

The functions are,

x=u-vandy=u+vfor0u2and0v1

02

Find the Jacobian

The Jacobian is computed as,

(x,y)(u,v)=detxuyuxvyv(x,y)(u,v)=det11-11(x,y)(u,v)=1-(-1)(x,y)(u,v)=1+1=2

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