Consider the initial value problem x₁ = 4x2, -4x1+8x2, x1(0) = 4, x2(0) = 7. x = Find the eigenvalue λ, an eigenvector v₁, and a generalized eigenvector 2 for the coefficient matrix of this linear system. λ = v₁ = [8] * = help (numbers) help (matrices) Find the most general real-valued solution to the linear system of differential equations. Use C1 and C2 to denote arbitrary constants, and enter them as "c1" and "c2". x1(t) = = help (formulas) x2(t) = = help (formulas) Solve the original initial value problem. x1(t) = = x2(t) = = help (formulas) help (formulas) Book: Section 3.7 of Notes on Diffy Qs
Consider the initial value problem x₁ = 4x2, -4x1+8x2, x1(0) = 4, x2(0) = 7. x = Find the eigenvalue λ, an eigenvector v₁, and a generalized eigenvector 2 for the coefficient matrix of this linear system. λ = v₁ = [8] * = help (numbers) help (matrices) Find the most general real-valued solution to the linear system of differential equations. Use C1 and C2 to denote arbitrary constants, and enter them as "c1" and "c2". x1(t) = = help (formulas) x2(t) = = help (formulas) Solve the original initial value problem. x1(t) = = x2(t) = = help (formulas) help (formulas) Book: Section 3.7 of Notes on Diffy Qs
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.2: Linear Independence, Basis, And Dimension
Problem 3AEXP
Related questions
Question
![Consider the initial value problem
x₁
=
4x2,
-4x1+8x2,
x1(0) = 4,
x2(0) = 7.
x =
Find the eigenvalue λ, an eigenvector v₁, and a generalized eigenvector 2 for the
coefficient matrix of this linear system.
λ
=
v₁ =
[8] *
=
help (numbers) help (matrices)
Find the most general real-valued solution to the linear system of differential equations. Use
C1 and C2 to denote arbitrary constants, and enter them as "c1" and "c2".
x1(t) =
=
help (formulas)
x2(t) =
=
help (formulas)
Solve the original initial value problem.
x1(t) =
=
x2(t) =
=
help (formulas)
help (formulas)
Book: Section 3.7 of Notes on Diffy Qs](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fed04f254-2b14-4f51-a897-ea8ba8024a7a%2Ff254d3b1-9c4a-431e-b16d-ae2209086e17%2Fvdv9x67_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider the initial value problem
x₁
=
4x2,
-4x1+8x2,
x1(0) = 4,
x2(0) = 7.
x =
Find the eigenvalue λ, an eigenvector v₁, and a generalized eigenvector 2 for the
coefficient matrix of this linear system.
λ
=
v₁ =
[8] *
=
help (numbers) help (matrices)
Find the most general real-valued solution to the linear system of differential equations. Use
C1 and C2 to denote arbitrary constants, and enter them as "c1" and "c2".
x1(t) =
=
help (formulas)
x2(t) =
=
help (formulas)
Solve the original initial value problem.
x1(t) =
=
x2(t) =
=
help (formulas)
help (formulas)
Book: Section 3.7 of Notes on Diffy Qs
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