7.1.39. On the vector space R³, let R denote counterclockwise rotation around the x axis by 90° and S counterclockwise rotation around the z-axis by 90°. (a) Find matrix representatives for R and S. (b) Show that RoS SOR. Explain what happens to the standard basis vectors under the two compositions. (c) Give an experimental demonstration of the noncommutativity of R and S by physically rotating a solid object, e.g., this book, in the prescribed manners.
7.1.39. On the vector space R³, let R denote counterclockwise rotation around the x axis by 90° and S counterclockwise rotation around the z-axis by 90°. (a) Find matrix representatives for R and S. (b) Show that RoS SOR. Explain what happens to the standard basis vectors under the two compositions. (c) Give an experimental demonstration of the noncommutativity of R and S by physically rotating a solid object, e.g., this book, in the prescribed manners.
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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7.1.39
Transcribed Image Text:7.1.39. On the vector space R³, let R denote counterclockwise rotation around the x axis
by 90° and S counterclockwise rotation around the z-axis by 90°. (a) Find matrix
representatives for R and S. (b) Show that RoS S°R. Explain what happens
to the standard basis vectors under the two compositions. (c) Give an experimental
demonstration of the noncommutativity of R and S by physically rotating a solid object,
e.g., this book, in the prescribed manners.
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