Suppose a system of differential equations can be written in matrix form as dx dt dy U dt x(t) = where A is a 3 x 3 matrix. = x = = Ay If A has eigenvalues 7, -1, 8 with corresponding eigenvectors y(t) z(t) = = Z general solution the system. (Use c₁ for terms involving eigenvalue 7, c₂ for terms involving eigenvalue - 1, and c3 for terms involving eigenvalue 8.) 400 -2 1 write the

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
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Homework 16:

Question 8

Suppose a system of differential equations can be written in matrix form as
*****
dx
dt
dy
dt
dz
dt
x
=
= Ay
where A is a 3 x 3 matrix.
If A has eigenvalues 7, -1,8 with corresponding eigenvectors
DOO-
-2
0
I
write the
general solution to the system.
(Use c₁ for terms involving eigenvalue 7, c₂ for terms involving eigenvalue –1, and c3 for terms
involving eigenvalue 8.)
x(t) =
y(t) =
z(t) =
Transcribed Image Text:Suppose a system of differential equations can be written in matrix form as ***** dx dt dy dt dz dt x = = Ay where A is a 3 x 3 matrix. If A has eigenvalues 7, -1,8 with corresponding eigenvectors DOO- -2 0 I write the general solution to the system. (Use c₁ for terms involving eigenvalue 7, c₂ for terms involving eigenvalue –1, and c3 for terms involving eigenvalue 8.) x(t) = y(t) = z(t) =
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