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Find all values of the angle (in radians, with 0 ≤ 0 < 2π) for which the matrix cos 8-sin 8 A = sin has real eigenvalues. (Enter your answers as a comma-separated list.) 0 = rad in oooo cos 0 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 The only rotations that send vectors to multiples of themselves are the identity and the 180° rotation. O There are no rotations that send vectors to multiples of themselves.

Find all values of the angle (in radians, with 0 ≤ 0 < 2π) for which the matrix cos 8-sin 8 A = sin has real eigenvalues. (Enter your answers as a comma-separated list.) 0 = rad in oooo cos 0 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 The only rotations that send vectors to multiples of themselves are the identity and the 180° rotation. O There are no rotations that send vectors to multiples of themselves.

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 (in radians, with 0 ≤ 0 < 2π) for which the matrix cos sin 8 sin 8 cos has real eigenvalues. (Enter your answers as a comma-separated list.) 8 = rad A = li li 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 The only rotations that send vectors to multiples of themselves are the identity and the 180° rotation. O There are no rotations that send vectors to multiples of themselves.
Transcribed Image Text:Find all values of the angle (in radians, with 0 ≤ 0 < 2π) for which the matrix cos sin 8 sin 8 cos has real eigenvalues. (Enter your answers as a comma-separated list.) 8 = rad A = li li 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 The only rotations that send vectors to multiples of themselves are the identity and the 180° rotation. O There are no rotations that send vectors to multiples of themselves.
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