Suppose a system of differential equations can be written in matrix form as dx dt dy dt dz dt = A x(t) = y(t) = z(t) = x where A is a 3 x 3 matrix. = Y 2 1 If A has eigenvalues 7, -1, 8 with corresponding eigenvectors -2 I 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.) write the
Suppose a system of differential equations can be written in matrix form as dx dt dy dt dz dt = A x(t) = y(t) = z(t) = x where A is a 3 x 3 matrix. = Y 2 1 If A has eigenvalues 7, -1, 8 with corresponding eigenvectors -2 I 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.) 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
dy
dt
dz
dt
=
x
Ay
where A is a 3 x 3 matrix.
y(t) =
z(t) =
Z
=
If A has eigenvalues 7, —1, 8 with corresponding eigenvectors -2
1
400-
1
I
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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