Find the general solution of the linear system (1) when A is the n x n diagonal matrix A = diag[Aj, A21... ,An]- What condition on the eigenvalues Al, ... , An will guarantee that limt_,,. x(t) = 0 for all solutions x(t) of (1)?

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.4: The Singular Value Decomposition
Problem 50EQ
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Find the general solution of the linear system (1) when A is the
n x n diagonal matrix A = diag[Aj, A21... ,An]- What condition on
the eigenvalues Al, ... , An will guarantee that limt_,,. x(t) = 0 for all
solutions x(t) of (1)?

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