3. Let D be the image of [1,4] × [1,4] under the transformation T(u, v) = (², ²).(a) Sketch the region D.(b) Use the change of variables formula to compute the area of D, i.e. compute1dA.

Answered: Image /qna-images/answer/c30567b8-add2-4a7c-8f28-f5711483fe6c.jpg

Answered: 3. Let D be the image of [1,4] × [1, 4]…

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Linear Transformations

Section6.1: Introduction To Linear Transformations

Problem 45E: Let T be a linear transformation from R2 into R2 such that T(x,y)=(xcosysin,xsin+ycos). Find a...

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Let T be a linear transformation from R2 into R2 such that T(x,y)=(xcosysin,xsin+ycos). Find a T(4,4) for =45, b T(4,4) for =30, and c T(5,0) for =120.
9. Let R be a square with vertices (0,0), (1,1), (2,0) and (1, -1) in the xy-plane. It might be useful/helpful to sketch the region R and the region S a) Find the image Sin the uv-plane under the transformation T: x=u + v, y = u - V hint: solve for u by solving for x + y (use system) b)Write the Jacobian Matrix of partial derivatives c) evaluate the determinant of the Jacobian d) Rewrite the integral using a change of variables to u and v with the Jacobian and evaluate the new integral. SSR xydA
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3. Let D be the image of [1,4] × [1, 4] under the transformation T(u, v) = (², ²). (a) Sketch the region D. (b) Use the change of variables formula to compute the area of D, i.e. compute 1dA.