sider the system of differential equations x= 10/3x1 + 4/3x2 x2 = 8/3x1 +14/3x2' ere 1 and 2 are functions of t. Our goal is first to find the general solution of this system and then a particular solution. v AV
sider the system of differential equations x= 10/3x1 + 4/3x2 x2 = 8/3x1 +14/3x2' ere 1 and 2 are functions of t. Our goal is first to find the general solution of this system and then a particular solution. v AV
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.7: The Inverse Of A Matrix
Problem 32E
Related questions
Question
![Consider the system of differential equations
ab sin (a)
where 1 and 2 are functions of t. Our goal is first to find the general solution of this system and then a particular solution.
a) This system can be written using matrices as X' = AX, where X is in R2 and the matrix A is
A =
əx
=
and
X₂=
8
Eigenvalues:
Give an eigenvector associated to the smallest eigenvalue.
Give an eigenvector associated to the largest eigenvalue.
Answer:
a Ω
b) Find the eigenvalues and eigenvectors of the matrix A associated to the system of linear differential equatons. List the eigenvalues separated
semicolons.
x₁ = 10/3x1 + 4/3x2
x=8/3x1 +14/3x2
c) The general solution of the system of linear differential equations is of the form X = c₁ X₁ + c2X2, where c₁ and co are constants, and
X1
Answer: X(t) = - (21 (6))
=
d) Find the solution if the initial condition is
-
B
"
We assume that X₁ is assoicated to the smallest eigenvalue and X2 to the largest eigenvalue. Use the scientific calculator notation. For instance 3e
written 3*e^(-4*t).
-3
(21) - (2³) at t
=
at t = 0.
-4t
is](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F114e9863-6405-4bfc-8c98-0cd00938b00b%2F677cf52b-c1d8-466c-92b8-b9a23e12ea54%2Fsqo20wg_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the system of differential equations
ab sin (a)
where 1 and 2 are functions of t. Our goal is first to find the general solution of this system and then a particular solution.
a) This system can be written using matrices as X' = AX, where X is in R2 and the matrix A is
A =
əx
=
and
X₂=
8
Eigenvalues:
Give an eigenvector associated to the smallest eigenvalue.
Give an eigenvector associated to the largest eigenvalue.
Answer:
a Ω
b) Find the eigenvalues and eigenvectors of the matrix A associated to the system of linear differential equatons. List the eigenvalues separated
semicolons.
x₁ = 10/3x1 + 4/3x2
x=8/3x1 +14/3x2
c) The general solution of the system of linear differential equations is of the form X = c₁ X₁ + c2X2, where c₁ and co are constants, and
X1
Answer: X(t) = - (21 (6))
=
d) Find the solution if the initial condition is
-
B
"
We assume that X₁ is assoicated to the smallest eigenvalue and X2 to the largest eigenvalue. Use the scientific calculator notation. For instance 3e
written 3*e^(-4*t).
-3
(21) - (2³) at t
=
at t = 0.
-4t
is
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
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 4 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
![Calculus For The Life Sciences](https://www.bartleby.com/isbn_cover_images/9780321964038/9780321964038_smallCoverImage.gif)
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
![Elementary Linear Algebra (MindTap Course List)](https://www.bartleby.com/isbn_cover_images/9781305658004/9781305658004_smallCoverImage.gif)
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
![Calculus For The Life Sciences](https://www.bartleby.com/isbn_cover_images/9780321964038/9780321964038_smallCoverImage.gif)
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
![Elementary Linear Algebra (MindTap Course List)](https://www.bartleby.com/isbn_cover_images/9781305658004/9781305658004_smallCoverImage.gif)
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
![Linear Algebra: A Modern Introduction](https://www.bartleby.com/isbn_cover_images/9781285463247/9781285463247_smallCoverImage.gif)
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning