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

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

Advanced Engineering Mathematics
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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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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