Transcribed Image Text:What is the general real solution?
O A. Re(x(t)) = C₁
B. Re(x(t)) = C₁
O c. Re(x(t)) = C₁
- 3 cos 9t-9 sin 9t
2 sin 9t
D. Re(x(t)) = C₁1
- 3 cos 9t + 9 sin 9t
2 sin 9t
- 3 cos 9t - 9 sin 9t
2 cos 9t
- 3 cos 9t+ 9 sin 9t
+ C₂
2 cos 9t
+₂[
+ C2
- 3 sin 9t + 9 cos 9t
2 cos 9t
18 ] + ₂[
Describe the shapes of typical trajectories of Re(x(t)). Choose the correct answer below.
- 3 sin 9t-9 cos 9t
2 cos 9t
- 3 sin 9t + 9 cos 9t
2 sin 9t
- 3 sin 9t-9 cos 9t
2 sin 9t
The trajectories spiral inward toward the origin.
The trajectories form ellipses around the origin.
The trajectories spiral outward away from the origin.
Transcribed Image Text:For matrix A below, construct the general solution of x' = Ax involving complex eigenfunctions and then obtain the general real solution. Describe the shapes of typical trajectories.
3
45
A-[-2-4)
=
3
What is the general solution involving complex eigenfunctions?
A. X(t) = C₁
B. X(t) = C₁
C. X(t) = C₁
O D. X(t) = C₁
- 3 - 9i
- 45
- 3+9i
2
- 3 - 9i
2
- 3+9i
- 45
e(9i)t
(9i)t + C₂
e(9i)t
+ C₂
e(9i)t
+ C₂
+ C2
- 3+9i
- 45
- 3-9i
2
- 3+9i
2
- 3-9i
- 45
(-9i)t
le(-9i)t
(-9i)t
- 9i)t
Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.
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![What is the general real solution?
O A. Re(x(t)) = C₁
B. Re(x(t)) = C₁
O c. Re(x(t)) = C₁
- 3 cos 9t-9 sin 9t
2 sin 9t
D. Re(x(t)) = C₁1
- 3 cos 9t + 9 sin 9t
2 sin 9t
- 3 cos 9t - 9 sin 9t
2 cos 9t
- 3 cos 9t+ 9 sin 9t
+ C₂
2 cos 9t
+₂[
+ C2
- 3 sin 9t + 9 cos 9t
2 cos 9t
18 ] + ₂[
Describe the shapes of typical trajectories of Re(x(t)). Choose the correct answer below.
- 3 sin 9t-9 cos 9t
2 cos 9t
- 3 sin 9t + 9 cos 9t
2 sin 9t
- 3 sin 9t-9 cos 9t
2 sin 9t
The trajectories spiral inward toward the origin.
The trajectories form ellipses around the origin.
The trajectories spiral outward away from the origin.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbe763e4e-f795-40b2-8fd9-57a3e5a9095e%2F82198109-4181-4aa0-a166-3fdc1f297651%2Fbwa1cj_processed.png&w=3840&q=75)
