x = 2x, +3x2 x = x, -5x2 2) %3D Given the systems 1) x = 2x, + X, x = x, - X, a) Write the system as a matrix equation. b) Find the eigenvalues and corresponding eigenvectors for your coefficient matrix. c) State the two eigenvalue solutions you get.

x = 2x, +3x2 x = x, -5x2 2) %3D Given the systems 1) x = 2x, + X, x = x, - X, a) Write the system as a matrix equation. b) Find the eigenvalues and corresponding eigenvectors for your coefficient matrix. c) State the two eigenvalue solutions you get.

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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Question

x = 2x, +3x,
x = 2x, +x2
x = X, -5x2
2)
x = x, - X,
Given the systems 1)
a) Write the system as a matrix equation.
b) Find the eigenvalues and corresponding eigenvectors for your coefficient matrix.
c) State the two eigenvalue solutions you get.
d) Verify your solutions in part c are linearly independent
e) State a general solution to the system.
) Use Mathematica to plot a slope field and solution curves.

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