Consider the linear system æ' = Ax, where A is a real 2 x 2 matrix with constant entries and repeated eigenvalues. Use the following information to determine A: The phase plane solution trajectories have horizontal tangents on the line a2 = 5x1 and vertical tangents on the line 21 = 0. Also, A has a nonzero repeated eigenvalue and a21 = 6. A = dx2 Hint: Consider when the parametric form of the derivatives: and 2 (t) a(t) are zero. da t r(t)

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 30E
icon
Related questions
Question
Consider the linear system æ ' = Ax, where A is a real 2 × 2 matrix with constant entries and repeated eigenvalues. Use the
following information to determine A:
The phase plane solution trajectories have horizontal tangents on the line x2 = 5x1 and vertical tangents on the line
X1 = 0.
%3D
Also, A has a nonzero repeated eigenvalue and a21
= 6.
A =
X2 (t)
and
dx2 lt
a'{ (t)
x (t)
a, (t)
dx1
dx2
Hint: Consider when the parametric form of the derivatives:
are zero.
dx1 lt
Transcribed Image Text:Consider the linear system æ ' = Ax, where A is a real 2 × 2 matrix with constant entries and repeated eigenvalues. Use the following information to determine A: The phase plane solution trajectories have horizontal tangents on the line x2 = 5x1 and vertical tangents on the line X1 = 0. %3D Also, A has a nonzero repeated eigenvalue and a21 = 6. A = X2 (t) and dx2 lt a'{ (t) x (t) a, (t) dx1 dx2 Hint: Consider when the parametric form of the derivatives: are zero. dx1 lt
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Knowledge Booster
Matrix Eigenvalues and Eigenvectors
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage