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,).

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Let R : R? → R² be rotation by
57
counter-clockwise around the origin, and S : R? → R? be reflection across the line y
6
-2x. Consider
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(e1), T(e2).

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