(d) State the corresponding eigenvalues in each case and write down the general solution of the system dX dt = AX .

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 32E
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Question
4.
Consider the system of homogenous linear differential equations
(a)
dx
dt
dy
dt
-=-2x+2y+2z
-=2x-5y+z
dz
-= 2x+y=z
dt
Write the system of equations in the form
dX
dt
= AX,
X
where X = y and identify the matrix A.
C
Z
Transcribed Image Text:4. Consider the system of homogenous linear differential equations (a) dx dt dy dt -=-2x+2y+2z -=2x-5y+z dz -= 2x+y=z dt Write the system of equations in the form dX dt = AX, X where X = y and identify the matrix A. C Z
(b) Show that
2
1 is an eigenvector.
1
8-B
(c) Show that a 1+B is an eigenvector for arbitrary values of the
-2
constants a and B.
(d) State the corresponding eigenvalues in each case and write down the general
solution of the system
dX
dt
= AX.
Transcribed Image Text:(b) Show that 2 1 is an eigenvector. 1 8-B (c) Show that a 1+B is an eigenvector for arbitrary values of the -2 constants a and B. (d) State the corresponding eigenvalues in each case and write down the general solution of the system dX dt = AX.
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