5. Find the standard matrix for the linear operator T: R³ R³ that first transform by the formula T(x, y, z) = (x-y+z, -x + y, y-z), then rotate the resulting vector anti clockwise about the z-axis through an angle = 120°, and then project the resulting vector about zx-plane. Hence compute T(1,0,1).
5. Find the standard matrix for the linear operator T: R³ R³ that first transform by the formula T(x, y, z) = (x-y+z, -x + y, y-z), then rotate the resulting vector anti clockwise about the z-axis through an angle = 120°, and then project the resulting vector about zx-plane. Hence compute T(1,0,1).
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter7: Eigenvalues And Eigenvectors
Section7.CM: Cumulative Review
Problem 11CM
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Question
![5. Find the standard matrix for the linear operator T: R R that first transform by the
formula T(x, y, z) = (x-y+ z,-x + y,y-z), then rotate the resulting vector anti
clockwise about the z-axis through an angle 0 = 120", and then project the resulting
vector about zx-plane. Hence compute T(1,0,1).
%3D
%3D](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F020773a0-69e9-4c03-ae1e-435434dba5d9%2F982e3d3c-9664-4300-aea8-823371f03aca%2Fm8vabgg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:5. Find the standard matrix for the linear operator T: R R that first transform by the
formula T(x, y, z) = (x-y+ z,-x + y,y-z), then rotate the resulting vector anti
clockwise about the z-axis through an angle 0 = 120", and then project the resulting
vector about zx-plane. Hence compute T(1,0,1).
%3D
%3D
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