A 2 x 2 matrix A has eigenvalues of -1 and 8 with corresponding eigenvectors of and respectively. Find the general solution to dx = Ax. dt
A 2 x 2 matrix A has eigenvalues of -1 and 8 with corresponding eigenvectors of and respectively. Find the general solution to dx = Ax. dt
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:A 2 x 2 matrix A has eigenvalues of -1 and 8 with corresponding eigenvectors of
and
respectively. Find the general solution to
dx
= Ax.
dt
Transcribed Image Text:Consider the system of equations
dx
(1)
A(t)x + b(t).
dt
Show that if x, is a solution for (1) and x, solves * = A(t)x, then x := x, + Xh solves (1). Explain
how you could use this to solve inhomogeneous systems.
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