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Perturbed Linear System

Consider the perturbed linear system

x' = (A + eB(t))x, x is an element of R^n,

where A is a constant matrix, B is a bounded continuous matrix valued function, and e is a small parameter. Assume that all eigenvalues of A have non-zero real part.

1) Show that the only bounded solution of the system is 0.

2) If A has an eigenvalue with zero real part, then is the above still true?

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Solution Summary

This is a proof regarding the bounded solution of a perturbed linear system. The solution is enclosed within a Word document.