Suppose a system of differential equations can be written in matrix form as Г dx * 3* ** dt dt dz dt = A x(t) = = where A is a 3 x 3 matrix. = 8 S y(t) = = z(t) = Z If A has eigenvalues 7, -1,8 with corresponding eigenvectors -2 000 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.) I write the
Suppose a system of differential equations can be written in matrix form as Г dx * 3* ** dt dt dz dt = A x(t) = = where A is a 3 x 3 matrix. = 8 S y(t) = = z(t) = Z If A has eigenvalues 7, -1,8 with corresponding eigenvectors -2 000 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.) I write the
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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
Transcribed Image Text:Suppose a system of differential equations can be written in matrix form as
dx
dt
dt
dz
dt
-
A
y(t) =
z(t) =
X
where A is a 3 x 3 matrix.
=
Y
Z
If A has eigenvalues 7, —1, 8 with corresponding eigenvectors
0·00
-2
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) =
write the
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