The general solution of the linear system X' = AX is given. -6 ^ - (-3 %). A -5 4 -t ()()()] x(t) = c₁ 1 -t e + te + 1 e (a) In this case discuss the nature of the solutions in a neighborhood of (0, 0). All solutions spiral toward (0, 0). O All solutions become unbounded and y = x serves as the asymptote. O All solutions approach (0, 0) from the direction specified by y = x. If X(0) = X lies on the line x = 0, then X(t) approaches (0, 0) along this line. Otherwise x(t) approaches (0, 0) from the direction determined by y = x. If X(0) = X lies on the line y = x, then X(t) approaches (0, 0) along this line. Otherwise x(t) approaches (0, 0) from the direction determined by x = 0. (b) With the aid of a calculator or a CAS graph the solution that satisfies X(0) = (1, 1). 1.5 y -1.5 -1.0 -0.5 (1, 1) 1.0 0.5 -0.5 -1.0 -1.5 y 1.5 1.0 0.5 y 1.5 (1, 1) 1.0 0.5 X 0.5 1.0 1.5 -1.5 -1.0 -0,5 -0.5 -1.0 -1.5 y 1.5 EX 0.5 1.0 1.5 1.0 (1, 1) 0.5 X -1.5 -1.0 -0.5 -1.5 -1.0 -0.5 0.5 1.0 1.5 -0.5 -0.5 -1.0 -1.5 ох -1.0 -1.5 X 0.5 1.0 1.5
The general solution of the linear system X' = AX is given. -6 ^ - (-3 %). A -5 4 -t ()()()] x(t) = c₁ 1 -t e + te + 1 e (a) In this case discuss the nature of the solutions in a neighborhood of (0, 0). All solutions spiral toward (0, 0). O All solutions become unbounded and y = x serves as the asymptote. O All solutions approach (0, 0) from the direction specified by y = x. If X(0) = X lies on the line x = 0, then X(t) approaches (0, 0) along this line. Otherwise x(t) approaches (0, 0) from the direction determined by y = x. If X(0) = X lies on the line y = x, then X(t) approaches (0, 0) along this line. Otherwise x(t) approaches (0, 0) from the direction determined by x = 0. (b) With the aid of a calculator or a CAS graph the solution that satisfies X(0) = (1, 1). 1.5 y -1.5 -1.0 -0.5 (1, 1) 1.0 0.5 -0.5 -1.0 -1.5 y 1.5 1.0 0.5 y 1.5 (1, 1) 1.0 0.5 X 0.5 1.0 1.5 -1.5 -1.0 -0,5 -0.5 -1.0 -1.5 y 1.5 EX 0.5 1.0 1.5 1.0 (1, 1) 0.5 X -1.5 -1.0 -0.5 -1.5 -1.0 -0.5 0.5 1.0 1.5 -0.5 -0.5 -1.0 -1.5 ох -1.0 -1.5 X 0.5 1.0 1.5
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section: Chapter Questions
Problem 3RE
Related questions
Question
![The general solution of the linear system X' = AX is given.
-6
^ - (-3 %).
A
-5 4
-t
()()()]
x(t) = c₁
1 -t
e +
te + 1 e
(a) In this case discuss the nature of the solutions in a neighborhood of (0, 0).
All solutions spiral toward (0, 0).
O All solutions become unbounded and y = x serves as the asymptote.
O
All solutions approach (0, 0) from the direction specified by y = x.
If X(0) = X lies on the line x = 0, then X(t) approaches (0, 0) along this line. Otherwise x(t) approaches (0, 0) from the direction
determined by y = x.
If X(0) = X lies on the line y = x, then X(t) approaches (0, 0) along this line. Otherwise x(t) approaches (0, 0) from the direction
determined by x = 0.
(b) With the aid of a calculator or a CAS graph the solution that satisfies X(0) = (1, 1).
1.5
y
-1.5 -1.0
-0.5
(1, 1)
1.0
0.5
-0.5
-1.0
-1.5
y
1.5
1.0
0.5
y
1.5
(1, 1)
1.0
0.5
X
0.5
1.0
1.5
-1.5 -1.0 -0,5
-0.5
-1.0
-1.5
y
1.5
EX
0.5
1.0
1.5
1.0
(1, 1)
0.5
X
-1.5 -1.0 -0.5
-1.5
-1.0
-0.5
0.5
1.0
1.5
-0.5
-0.5
-1.0
-1.5
ох
-1.0
-1.5
X
0.5
1.0
1.5](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb3b2a629-b543-4446-b89d-eb00585aef9b%2F424d7fdd-9977-4a0c-a32f-3d1f056b3023%2F0v7w7p_processed.png&w=3840&q=75)
Transcribed Image Text:The general solution of the linear system X' = AX is given.
-6
^ - (-3 %).
A
-5 4
-t
()()()]
x(t) = c₁
1 -t
e +
te + 1 e
(a) In this case discuss the nature of the solutions in a neighborhood of (0, 0).
All solutions spiral toward (0, 0).
O All solutions become unbounded and y = x serves as the asymptote.
O
All solutions approach (0, 0) from the direction specified by y = x.
If X(0) = X lies on the line x = 0, then X(t) approaches (0, 0) along this line. Otherwise x(t) approaches (0, 0) from the direction
determined by y = x.
If X(0) = X lies on the line y = x, then X(t) approaches (0, 0) along this line. Otherwise x(t) approaches (0, 0) from the direction
determined by x = 0.
(b) With the aid of a calculator or a CAS graph the solution that satisfies X(0) = (1, 1).
1.5
y
-1.5 -1.0
-0.5
(1, 1)
1.0
0.5
-0.5
-1.0
-1.5
y
1.5
1.0
0.5
y
1.5
(1, 1)
1.0
0.5
X
0.5
1.0
1.5
-1.5 -1.0 -0,5
-0.5
-1.0
-1.5
y
1.5
EX
0.5
1.0
1.5
1.0
(1, 1)
0.5
X
-1.5 -1.0 -0.5
-1.5
-1.0
-0.5
0.5
1.0
1.5
-0.5
-0.5
-1.0
-1.5
ох
-1.0
-1.5
X
0.5
1.0
1.5
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 1 images
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning