A linear transformation T : R² → R² first reflects points through the x1-axis and then reflects points through the x2- axis. Show that T can also be described as a linear transfor- mation that rotates points about the origin. What is the angle of that rotation?

A linear transformation T : R² → R² first reflects points through the x1-axis and then reflects points through the x2- axis. Show that T can also be described as a linear transfor- mation that rotates points about the origin. What is the angle of that rotation?

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 39E: For the linear transformation from Exercise 33, find a T(1,1), b the preimage of (1,1), and c the...

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Solve the problem given in image

A linear transformation T : R² → R? first reflects points
through the x1-axis and then reflects points through the x2-
axis. Show that T can also be described as a linear transfor-
mation that rotates points about the origin. What is the angle
of that rotation?

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