T1 = “rotation through 90◦ clockwise”T2 = “horizontal shear with factor 1 ”T3 = “rotation through 90◦ anti-clockwise”(a) Write down the matrices A1, A2, A3 that correspond to the respective transfor- mations.(b) Use matrix multiplication to determine the combined geometric effect of T1 followed by T2 followed by T3. Describe the geometric effect.(c) Use matrix multiplication to determine the combined geometric effect of T2 followed by T1 followed by T3, and compare it with the result from (b).

The rotation transformation matrix is cosθ-sinθsinθcosθ The horizontal shear transformation matrix…

Answered: T1 = “rotation through 90◦ clockwise”…

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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T1 = “rotation through 90◦ clockwise”
T2 = “horizontal shear with factor 1 ”
T3 = “rotation through 90◦ anti-clockwise”

(a) Write down the matrices A1, A2, A3 that correspond to the respective transfor- mations.
(b) Use matrix multiplication to determine the combined geometric effect of T1 followed by T2 followed by T3. Describe the geometric effect.
(c) Use matrix multiplication to determine the combined geometric effect of T2 followed by T1 followed by T3, and compare it with the result from (b).

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