Let X(t) be a fundamental matrix for x′ = A(t)x on the interval I. Q. If t0 ∈ I, show that the solution to the initial-value problem x′= Ax, x(t0)=x0, can be written as x= X(t)X−1(t0)x0
Let X(t) be a fundamental matrix for x′ = A(t)x on the interval I. Q. If t0 ∈ I, show that the solution to the initial-value problem x′= Ax, x(t0)=x0, can be written as x= X(t)X−1(t0)x0
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.4: Similarity And Diagonalization
Problem 50EQ
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Let X(t) be a fundamental matrix for x′ = A(t)x on the interval I.
Q. If t0 ∈ I, show that the solution to the initial-value problem x′= Ax, x(t0)=x0, can be written as x= X(t)X−1(t0)x0
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