Show that e, = [1 2 3] is an eigenvector of the matrix A and find its corresponding eigenvalue. Find the other two eigenvalues and their corresponding eigenvectors. Write down in spectral form the general solution of the system of differential equations 2dx=7x-y-z = 4x - y 2=-3x+3y +z Hence show that if x = 2, y = 4 and z = 6 when t=0 then the solution is x = 2e', y = 4e', z = 6e¹ 712 I T + NIW MIN -12
Show that e, = [1 2 3] is an eigenvector of the matrix A and find its corresponding eigenvalue. Find the other two eigenvalues and their corresponding eigenvectors. Write down in spectral form the general solution of the system of differential equations 2dx=7x-y-z = 4x - y 2=-3x+3y +z Hence show that if x = 2, y = 4 and z = 6 when t=0 then the solution is x = 2e', y = 4e', z = 6e¹ 712 I T + NIW MIN -12
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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Include all steps.
![Show that e, = [1 2 3] is an eigenvector of
the matrix
A=
and find its corresponding eigenvalue. Find the
other two eigenvalues and their corresponding
eigenvectors.
Write down in spectral form the general
solution of the system of differential
equations
2dx = 7x-y-z
dt
dy
= 4x - y
dr
2 = −3x + 3y +z
dt
Hence show that if x = 2, y = 4 and z = 6
when t = =0 then the solution is
x = 2e',
y = 4e',
z = 6e¹
||
MIN
NIW
Ï](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd5d415d7-2c25-4f1c-be46-a3f9bc68c0c9%2Fd4e8483a-96f6-4bc0-bc14-6fd6c890bd10%2F6otej4_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Show that e, = [1 2 3] is an eigenvector of
the matrix
A=
and find its corresponding eigenvalue. Find the
other two eigenvalues and their corresponding
eigenvectors.
Write down in spectral form the general
solution of the system of differential
equations
2dx = 7x-y-z
dt
dy
= 4x - y
dr
2 = −3x + 3y +z
dt
Hence show that if x = 2, y = 4 and z = 6
when t = =0 then the solution is
x = 2e',
y = 4e',
z = 6e¹
||
MIN
NIW
Ï
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