Graphs of linear systems, Consider the linear system x' =

Graphs of linear systems

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Reference no: EM13122261

Consider the linear system x' = Ax, where A is a n x n real matrix. If x = x(t) is a solution of the linear system, we define:

G(x) = {x(t) : t E R),

which is the set of points on the solution curves x=x(t) in R^n. The set G(t) is called the graph of x = x(t) .

Show that if x(1) = x(1)(t) and x(2) = x(2)(t) are any two solutions of the linear system, then either the intersection of G(x1) and G(x2) is empty, or G(x1) = G(x2), that is their graphs are either disjointed or the same.

Reference no: EM13122261

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