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

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

Advanced Engineering Mathematics
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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Find all values of the angle 0 (in radians, with 0 <e < 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 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. 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.
Transcribed Image Text:Find all values of the angle 0 (in radians, with 0 <e < 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 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. 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.
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