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6. Let the n x n matrix A have real, distinct eigenvalues. Let (t, xo) be the solution of the initial value problem Show that for each fixed t E R. * = Ax, x(0) = Xo. محاد limy-x, (t, yo) = (t, xo). Yo This shows that the solution (t, xo) is a continuous function of the initial condition.

6. Let the n x n matrix A have real, distinct eigenvalues. Let (t, xo) be the solution of the initial value problem Show that for each fixed t E R. * = Ax, x(0) = Xo. محاد limy-x, (t, yo) = (t, xo). Yo This shows that the solution (t, xo) is a continuous function of the initial condition.

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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6. Let the n x n matrix A have real, distinct eigenvalues. Let (t, xo) be the solution of the initial value problem Show that for each fixed t E R. * = Ax, x(0) = Xo. limy-xo (t, yo) = (t, xo). This shows that the solution (t, xo) is a continuous function of the initial condition. ang pag
Transcribed Image Text:6. Let the n x n matrix A have real, distinct eigenvalues. Let (t, xo) be the solution of the initial value problem Show that for each fixed t E R. * = Ax, x(0) = Xo. limy-xo (t, yo) = (t, xo). This shows that the solution (t, xo) is a continuous function of the initial condition. ang pag
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