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Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.3: Lines

Problem 21E

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Question

Frequently, we encounter a need for two (different) linear transformations to transform a parallelogram
into a rectangular region. When this happens, we need to make choices like: u = -x + 5y and
v = 7x - 5y.
For this example, find the inverse transformations:
x =
=
u+v
6
7u+6
30
X
and use these to calculate the Jacobian:
a(x, y)
a(u, v)
30
0.233333
333333u + 0.033333
33333v

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