Let R : R? → R² be rotation by counter-clockwise around the origin, and S: R? → R² be reflection across the line y = -2x. Consider 6 the transformation given by T = S o Ro S. (a) Find the matrix for T. (b) Sketch a visualization of T, showing the unit square on one set of axes and its image under the transformation T on a separate set of axes. (c) Find the area of the parallelogram spanned by T(e,), T(e,).
Let R : R? → R² be rotation by counter-clockwise around the origin, and S: R? → R² be reflection across the line y = -2x. Consider 6 the transformation given by T = S o Ro S. (a) Find the matrix for T. (b) Sketch a visualization of T, showing the unit square on one set of axes and its image under the transformation T on a separate set of axes. (c) Find the area of the parallelogram spanned by T(e,), T(e,).
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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