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A rectangular x'y' z'-coordinate system is obtained by rotating an xyz-coordinate system counterclockwise about the y-axis through an angle € (looking along the positive y-axis toward the origin). Find a matrix A such that = A X Y 2 where (x, y, z) and (x', y', z') are the coordinates of the same point in the xyz- and x'y' z'-systems, respectively.

A rectangular x'y' z'-coordinate system is obtained by rotating an xyz-coordinate system counterclockwise about the y-axis through an angle € (looking along the positive y-axis toward the origin). Find a matrix A such that = A X Y 2 where (x, y, z) and (x', y', z') are the coordinates of the same point in the xyz- and x'y' z'-systems, respectively.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.7: The Inverse Of A Matrix
Problem 31E
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A rectangular x'y' z'-coordinate system is obtained by rotating an xyz-coordinate system counterclockwise about the y-axis through an angle (looking along the positive y-axis toward the origin). Find a matrix A such that 1-40 = Ay where (x, y, z) and (x', y', z') are the coordinates of the same point in the xyz- and x'y' z'-systems, respectively.
Transcribed Image Text:A rectangular x'y' z'-coordinate system is obtained by rotating an xyz-coordinate system counterclockwise about the y-axis through an angle (looking along the positive y-axis toward the origin). Find a matrix A such that 1-40 = Ay where (x, y, z) and (x', y', z') are the coordinates of the same point in the xyz- and x'y' z'-systems, respectively.
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