A translation in R2 is a function of the form T(x, y) = (x − h, y − k), where at least one of the constants h and k is nonzero.(a) Show that a translation in R2 is not a linear transformation.(b) For the translation T(x, y) = (x − 2, y + 1), determine the images of (0, 0), (2, −1), and (5, 4).(c) Show that a translation in R2 has no fixed points.
A translation in R2 is a function of the form T(x, y) = (x − h, y − k), where at least one of the constants h and k is nonzero.(a) Show that a translation in R2 is not a linear transformation.(b) For the translation T(x, y) = (x − 2, y + 1), determine the images of (0, 0), (2, −1), and (5, 4).(c) Show that a translation in R2 has no fixed points.
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 76E: A translation in R2 is a function of the form T(x,y)=(xh,yk), where at least one of the constants h...
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A translation in R2 is a function of the form T(x, y) = (x − h, y − k), where at least one of the constants h and k is nonzero.
(a) Show that a translation in R2 is not a linear transformation.
(b) For the translation T(x, y) = (x − 2, y + 1), determine the images of (0, 0), (2, −1), and (5, 4).
(c) Show that a translation in R2 has no fixed points.
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