Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
For the system of differential equations, - -9 1 _3] x + [ -¹ + ] y 8 a) Find the characteristic polynomial of the matrix of coefficients A. CA(X) b) Find the eigenvalues of A. Enter the eigenvalues as a list in ascending order separated by commas. A1, A2 = U1 = y' U2 = -7 = c) Find the eigenvectors assuming u₁ is the eigenvector associated with the smaller eigenvalue X₁ and u₂ is the eigenvector associated with the larger eigenvalue A₂. Enter the eigenvectors as a matrix with an appropriate size. 6

For the system of differential equations, - -9 1 _3] x + [ -¹ + ] y 8 a) Find the characteristic polynomial of the matrix of coefficients A. CA(X) b) Find the eigenvalues of A. Enter the eigenvalues as a list in ascending order separated by commas. A1, A2 = U1 = y' U2 = -7 = c) Find the eigenvectors assuming u₁ is the eigenvector associated with the smaller eigenvalue X₁ and u₂ is the eigenvector associated with the larger eigenvalue A₂. Enter the eigenvectors as a matrix with an appropriate size. 6

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
icon
Related questions
Question
For the system of differential equations, []+[4] y 6 8 a) Find the characteristic polynomial of the matrix of coefficients A. CA(X) A1, A2 = U₁ = = b) Find the eigenvalues of A. Enter the eigenvalues as a list in ascending order separated by commas. U₂ = c) Find the eigenvectors assuming u₁ is the eigenvector associated with the smaller eigenvalue X₁ and u₂ is the eigenvector associated with the larger eigenvalue A₂. Enter the eigenvectors as a matrix with an appropriate size. v(t) y' = d) Determine a general solution to the system by completing the following steps. i. Find v(t) = = [y−¹(t)f(t)dt . yp(t) = -7 y (t) ii. Find a particular solution y(t). = ii. Then a general solution for the system in the matrix form is
Transcribed Image Text:For the system of differential equations, []+[4] y 6 8 a) Find the characteristic polynomial of the matrix of coefficients A. CA(X) A1, A2 = U₁ = = b) Find the eigenvalues of A. Enter the eigenvalues as a list in ascending order separated by commas. U₂ = c) Find the eigenvectors assuming u₁ is the eigenvector associated with the smaller eigenvalue X₁ and u₂ is the eigenvector associated with the larger eigenvalue A₂. Enter the eigenvectors as a matrix with an appropriate size. v(t) y' = d) Determine a general solution to the system by completing the following steps. i. Find v(t) = = [y−¹(t)f(t)dt . yp(t) = -7 y (t) ii. Find a particular solution y(t). = ii. Then a general solution for the system in the matrix form is
Expert Solution
steps

Step by step

Solved in 3 steps with 4 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Calculus For The Life Sciences
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
SEE MORE TEXTBOOKS