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Consider the differential equation x\' = Ax. where A R3 times 3 has 3 different

ID: 3079637 • Letter: C

Question

Consider the differential equation x' = Ax. where A R3 times 3 has 3 different eigenvalues mu 1, mu 2, mu 3 and corresponding eigenvectors P1, P2, P3. Then a fundamental matrix for the system can be written where P er is a matrix with the eigenvectors p1, p2, p3 written in this order in the columns of the matrix. Show that Show that the transition matrix Phi(t, t0) can be written in the form Conclude that Phi(t, t0) = eA(t - t0) = eA (t - t0) (hint: sja daemi 7-9 a daemabla i 6). Note: this is true in any dimension if the matrix A has n linearly independent eigenvectors.

Explanation / Answer

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