6 - cos t sin t cos t Let 1 (t) , 02(t) cos t, a3 (t) = - sin t Which of the following statements are true? sin t cos t I. The Wronskian of a1(t), a2(t), r3 (t) is W(r1, x2, r3)(t) = cos t. II. æ1 (t), x2(t), x3(t) are linearly independent on (-0o, 0). III. 1(t), 2(t), x3 (t) are solutions of a linear homogeneous system a' (t) = A(t)x(t) on (-0o, 00), where A(t) is a 3 x 3 matrix function continuous on (-0o, 00). %3D a) O I, Il and III b) O Only I c) O I and I| d) O Il and II e) I and III Boş bırak
6 - cos t sin t cos t Let 1 (t) , 02(t) cos t, a3 (t) = - sin t Which of the following statements are true? sin t cos t I. The Wronskian of a1(t), a2(t), r3 (t) is W(r1, x2, r3)(t) = cos t. II. æ1 (t), x2(t), x3(t) are linearly independent on (-0o, 0). III. 1(t), 2(t), x3 (t) are solutions of a linear homogeneous system a' (t) = A(t)x(t) on (-0o, 00), where A(t) is a 3 x 3 matrix function continuous on (-0o, 00). %3D a) O I, Il and III b) O Only I c) O I and I| d) O Il and II e) I and III Boş bırak
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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Question
Transcribed Image Text:6 -
cos t
sin t
cos t
Let 1 (t)
, x2(t) = | cos t , æ3(t)
- sin t
Which of the following statements are true?
sin t
cos t
I. The Wronskian of 1(t), x2(t), c3(t) is W(r1, 2, a3)(t)
II. #1 (t), x2(t), x3(t) are linearly independent on (-o, o0).
II. a1(t), x2(t), x3 (t) are solutions of a linear homogeneous system æ' (t) = A(t)x(t) on (-00, 00), where
A(t) is a 3 x 3 matrix function continuous on (-0o, 00).
= cos t.
%3D
a) O I, Il and II
b)
Only I
c) O I and Il
d)
Il and III
e) I and II
Cevap Listesi
Boş bırak
7.
7.
Карat
13
KÖnceki
6/13
Sonraki>
Akt
decen
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