(a) Find an affine change of coordinates that takes the unit square with vertices in the uv-plane to the rectangle with vertices in the xy-plane. x = x(u, v) = y = y(u, v) = d(x, y) d(u, v) P* = (0,0), Q* = (1,0), R* = (0, 1), S* = (1, 1) (b) Find the absolute value of the determinant of the Jacobian for this change of coordinates. = [det P = (-3,4), Q = (-1,4), R = (-3,7), S = (-1,7)

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section: Chapter Questions
Problem 41RE
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(a) Find an affine change of coordinates that takes the unit square with vertices
in the uv-plane to the rectangle with vertices
in the xy-plane.
X = : x(u, v) =
y = y(u, v) =
P* = (0,0), Q* = (1,0), R* = (0, 1), S* = (1, 1)
d(x, y)
|Kur p| = |det
d(u, v)
P = (−3, 4), Q = (−1,4), R = (−3, 7), S = (−1,7)
(b) Find the absolute value of the determinant of the Jacobian for this change of coordinates.
II
Transcribed Image Text:(a) Find an affine change of coordinates that takes the unit square with vertices in the uv-plane to the rectangle with vertices in the xy-plane. X = : x(u, v) = y = y(u, v) = P* = (0,0), Q* = (1,0), R* = (0, 1), S* = (1, 1) d(x, y) |Kur p| = |det d(u, v) P = (−3, 4), Q = (−1,4), R = (−3, 7), S = (−1,7) (b) Find the absolute value of the determinant of the Jacobian for this change of coordinates. II
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