Find all values of the angle 0 (in radians, with 0 ≤ 0 < 2π) for which the matrix -[ cos 0 -sin 0 sin e 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.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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4. [-/10 Points]
DETAILS
A =
Find all values of the angle 8 (in radians, with 0 ≤ 0 < 2π) for which the matrix
cos
sin 0
sin 0
cos e
has real eigenvalues. (Enter your answers as a comma-separated list.)
0 =
LARLINALG8 7.1.078.
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:4. [-/10 Points] DETAILS A = Find all values of the angle 8 (in radians, with 0 ≤ 0 < 2π) for which the matrix cos sin 0 sin 0 cos e has real eigenvalues. (Enter your answers as a comma-separated list.) 0 = LARLINALG8 7.1.078. 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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