A 3×3 real matrix has three eigenvalues. One of them is >₁ = -1 with eigenvector v₁ = -(0) Another is X2 = 1 + i with eigenvector v2 = (c) Find the solution to x' = (1) i (a) What is the third eigenvalue and its corresponding eigenvector? (b) Find the general solution to x' = Ax, in purely real form. Ax subject to initial condition x (0) : = (9)

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.1: Introduction To Eigenvalues And Eigenvectors
Problem 38EQ
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A 3×3 real matrix has three eigenvalues. One of them is λ₁
=
Another is A₂ = 1 + i with eigenvector v2
- (3)
=
-1 with eigenvector v₁ =
(a) What is the third eigenvalue and its corresponding eigenvector?
(b) Find the general solution to x'
=
Ax, in purely real form.
(c) Find the solution to x' = Ax subject to initial condition x (0)
=
(:).
(6)
1
Transcribed Image Text:A 3×3 real matrix has three eigenvalues. One of them is λ₁ = Another is A₂ = 1 + i with eigenvector v2 - (3) = -1 with eigenvector v₁ = (a) What is the third eigenvalue and its corresponding eigenvector? (b) Find the general solution to x' = Ax, in purely real form. (c) Find the solution to x' = Ax subject to initial condition x (0) = (:). (6) 1
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