Let X be the matrix function cos( 2 1) sin (2t) sin (21) -cos( 21) X (t) = Determine if X is a fundamental matrix for system x'= Ax with -2 A= 2 If so, find the solution of the system that satisfies 4 x(0) = cos( 2t) =4 sin (21) sin (21) - cos( 21) cos( 2 1) sin (2t) || b) О sin(2t) + -cos( 2t) Not a fundamental solution set. cos( 21) sin (2t) +4 d) sin (2t) -cos( 2 t) cos( 2t) + 2 sin(2t) sin (2t) - cos( 2 t) e) О
Let X be the matrix function cos( 2 1) sin (2t) sin (21) -cos( 21) X (t) = Determine if X is a fundamental matrix for system x'= Ax with -2 A= 2 If so, find the solution of the system that satisfies 4 x(0) = cos( 2t) =4 sin (21) sin (21) - cos( 21) cos( 2 1) sin (2t) || b) О sin(2t) + -cos( 2t) Not a fundamental solution set. cos( 21) sin (2t) +4 d) sin (2t) -cos( 2 t) cos( 2t) + 2 sin(2t) sin (2t) - cos( 2 t) e) О
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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![Let X be the matrix function
cos( 2 1) sin (2t)
sin (2t) -cos( 2 t)
X (t) =
Determine if X is a fundamental matrix for system x'= Ax with
0 -2
A=
2
If so, find the solution of the system that satisfies
4
x(0) =
cos( 2 t)
=4
sin (21)
sin(2t)
-cos( 2t)
cos( 21)
sin (2t)
sin(2t)
+
b) О
-cos( 21)
Not a fundamental solution set.
sin (2t)
+4
cos( 2t)
d)
sin(2t)
-cos( 2t)
cos( 2 t)
sin(2t)
+ 2
sin (2t)
- cos( 2 t)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F88afae02-80d5-49da-ad82-a7933e6f4445%2F23301aa7-12cd-4e2c-8f98-ff40026e9e88%2F653s5fk_processed.png&w=3840&q=75)
Transcribed Image Text:Let X be the matrix function
cos( 2 1) sin (2t)
sin (2t) -cos( 2 t)
X (t) =
Determine if X is a fundamental matrix for system x'= Ax with
0 -2
A=
2
If so, find the solution of the system that satisfies
4
x(0) =
cos( 2 t)
=4
sin (21)
sin(2t)
-cos( 2t)
cos( 21)
sin (2t)
sin(2t)
+
b) О
-cos( 21)
Not a fundamental solution set.
sin (2t)
+4
cos( 2t)
d)
sin(2t)
-cos( 2t)
cos( 2 t)
sin(2t)
+ 2
sin (2t)
- cos( 2 t)
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