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Find all values of the angle 0 (in radians, with 0 < 0 < 2n) for which the matrix cos e -sin e sin e cos e A has real eigenvalues. (Enter your answers as a comma-separated list.) = rad

Find all values of the angle 0 (in radians, with 0 < 0 < 2n) for which the matrix cos e -sin e sin e cos e A has real eigenvalues. (Enter your answers as a comma-separated list.) = rad

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter7: Eigenvalues And Eigenvectors
Section7.1: Eigenvalues And Eigenvectors
Problem 78E: Find all values of the angle for which the matrix A=[cossinsincos] has real eigenvalues. Interpret...
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Find all values of the angle 0 (in radians, with 0 < 0 < 2n) for which the matrix cos e -sin 0 A = sin 0 cos e has real eigenvalues. (Enter your answers as a comma-separated list.) rad Interpret your answer geometrically. O The only rotation that sends vectors to multiples of themselves is the 180° rotation. O The only rotation that sends vectors to multiples of themselves is the identity rotation. O There are no rotations that send vectors to multiples of themselves. O The only rotations that send vectors to multiples of themselves are the identity and the 180° rotation.
Transcribed Image Text:Find all values of the angle 0 (in radians, with 0 < 0 < 2n) for which the matrix cos e -sin 0 A = sin 0 cos e has real eigenvalues. (Enter your answers as a comma-separated list.) rad Interpret your answer geometrically. O The only rotation that sends vectors to multiples of themselves is the 180° rotation. O The only rotation that sends vectors to multiples of themselves is the identity rotation. O There are no rotations that send vectors to multiples of themselves. O The only rotations that send vectors to multiples of themselves are the identity and the 180° rotation.
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