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Find all values of the angle 0 (in radians, with 0 ≤ 0 < 2π) for which the matrix 9] cos 0 sin 0 cos e has real eigenvalues. (Enter your answers as a comma-separated list.) 0 = A = -sin 0 rad Interpret your answer geometrically. O There are no rotations that send vectors to multiples of themselves. O The only rotation that sends vectors to multiples of themselves is the identity rotation. 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.

Find all values of the angle 0 (in radians, with 0 ≤ 0 < 2π) for which the matrix 9] cos 0 sin 0 cos e has real eigenvalues. (Enter your answers as a comma-separated list.) 0 = A = -sin 0 rad Interpret your answer geometrically. O There are no rotations that send vectors to multiples of themselves. O The only rotation that sends vectors to multiples of themselves is the identity rotation. 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.

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 8 (in radians, with 0 ≤ 0 < 2π) for which the matrix cos Ꮎ -sin Ꮎ [ sin 0 cos 0 has real eigenvalues. (Enter your answers as a comma-separated list.) 0 = A = rad Interpret your answer geometrically. O There are no rotations that send vectors to multiples of themselves. O The only rotation that sends vectors to multiples of themselves is the identity rotation. 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.
Transcribed Image Text:Find all values of the angle 8 (in radians, with 0 ≤ 0 < 2π) for which the matrix cos Ꮎ -sin Ꮎ [ sin 0 cos 0 has real eigenvalues. (Enter your answers as a comma-separated list.) 0 = A = rad Interpret your answer geometrically. O There are no rotations that send vectors to multiples of themselves. O The only rotation that sends vectors to multiples of themselves is the identity rotation. 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.
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