Answered: e following systems, the origin is the… | bartleby

Algebra & Trigonometry with Analytic Geometry

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

See similar textbooks

Related questions

Question

Parts B, E, F. I attached a photo of the answered parts.

For the following systems, the origin is the equilibrium point.
dx
a) Write each system in matrix form = Ax.
dt
b)
Determine the eigenvalues of A.
c) State whether the origin is a stable or unstable equilibrium.
d) State whether the origin is a node, saddle point, spiral point, or center.
e) State the equations of the straight-line trajectories and tell whether they are going
towards or away from the origin. If none exist, state so.
f) If A has real eigenvalues, then determine the eigenvectors and use diagonalization to
solve the system. (See examples in Section 7.4)
3.
dx
dt
dt
= 4x - 13y
= 2x - 6y

dx
3) de
a)
a
1>
dy
dt
= 4x-13
F) stable
2x-6y
A = [
2
2
4
-120
d (x)
-13
[2²] [23] [4]
2]
ما

Expert Solution

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Blurred answer

Similar questions

Solve for x and y in the matrix equation 2AB=I, given A=[1123] and B=[x2y5].
Consider the system of linear equations in x and y. ax+by=ecx+dy=f Under what conditions will the system have exactly one solution?
For the following systems, the origin is the equilibrium point. a) Write each system in matrix form Ax. b) Determine the eigenvalues of A. c) State whether the origin is a stable or unstable equilibrium. d) State whether the origin is a node, saddle point, spiral point, or center. e) State the equations of the straight-line trajectories and tell whether they are going towards or away from the origin. If none exist, state so. f) If A has real eigenvalues, then determine the eigenvectors and use diagonalization to solve the system. (See examples in Section 7.4) 1. dx dt dy dt = -2x + 5cy 4y = dx dt C = 3
For the following systems, the origin is the equilibrium point. a) Write each system in matrix form b) Determine the eigenvalues of A. c) State whether the origin is a stable or unstable equilibrium. d) State whether the origin is a node, saddle point, spiral point, or center. e) State the equations of the straight-line trajectories and tell whether they are going towards or away from the origin. If none exist, state so. 4. f) If A has real eigenvalues, then determine the eigenvectors and use diagonalization to solve the system. (See examples in Section 7.4) dx dt dy dt = x + 4y dt = 4x + y = Ax.
For the following systems, the origin is the equilibrium point. a) Write each system in matrix form b) Determine the eigenvalues of A. c) State whether the origin is a stable or unstable equilibrium. d) State whether the origin is a node, saddle point, spiral point, or center. State the equations of the straight-line trajectories and tell whether they are going towards or away from the origin. If none exist, state so. f) If A has real eigenvalues, then determine the eigenvectors and use diagonalization to solve the system. (See examples in Section 7.4) 2. dx dt dy dt = 5x + 2y = 2x + 5y (Ctrl) dx dt = Ax.
For the following systems, the origin is the equilibrium point. dx a) Write each system in matrix form = Ax. dt b) Determine the eigenvalues of A. c) State whether the origin is a stable or unstable equilibrium. d) State whether the origin is a node, saddle point, spiral point, or center. e) State the equations of the straight-line trajectories and tell whether they are going towards or away from the origin. If none exist, state so. f) If A has real eigenvalues, then determine the eigenvectors and use diagonalization to solve the system. (See examples in Section 7.4) 6. dx dt dy dt = 2x - 8y = x - 2y
A box containing five, ten, and twenty-dollar bills, has 130 bills in it with a total value of $2560. Find how many bills of each type are in the box by setting up and solving a system of linear equations.
Show your complete solution
Determine which of the points (-3, 1, −1), (5, 6, 4), and (6, -3, 3) satisfy the linear system 2x2 + 5x3 -34 9x1 -X1 + 4x2 2x3 9 = Answer: = Save a little time and good practice. Consider this in the matrix-vector form A = 6 and enter A in calculator or octave and then calculate A for each given vector (written as a column vector)
Suppose the solution set of a system of linear equations can be described as x₁ = 2-5x4 x₂ = -4x4 x3 = 5 +9x4 with 4 free. a. Write the solution to this system in parametric vector form. x = DNE x+x4
Consider a system represented by a matrix equation in the form Xn+1 = TXn, Where i) Find the eigenvalues and the corresponding eigenvectors. ii) Write the form of the general solution and predict the long term behavior of the system.
b) Determine whether the matrices L-, ), M = [ - 3 - 2 2 4 3 L= , ), M = and N = , | -2 2 are linearly independent or not. Note: Use Gaussian elimination to solve the linear system and show all the steps in solving the linear system.

SEE MORE QUESTIONS

Recommended textbooks for you

Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:

9781133382119

Author:

Swokowski

Publisher:

Cengage

Linear Algebra: A Modern Introduction

Linear Algebra: A Modern Introduction

Algebra

ISBN:

9781285463247

Author:

David Poole

Publisher:

Cengage Learning

Elementary Linear Algebra (MindTap Course List)

Elementary Linear Algebra (MindTap Course List)

Algebra

ISBN:

9781305658004

Author:

Ron Larson

Publisher:

Cengage Learning

Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:

9781133382119

Author:

Swokowski

Publisher:

Cengage

Linear Algebra: A Modern Introduction

Linear Algebra: A Modern Introduction

Algebra

ISBN:

9781285463247

Author:

David Poole

Publisher:

Cengage Learning

Elementary Linear Algebra (MindTap Course List)

Elementary Linear Algebra (MindTap Course List)

Algebra

ISBN:

9781305658004

Author:

Ron Larson

Publisher:

Cengage Learning

SEE MORE TEXTBOOKS