Let M be a 3 x3 matrix with eigenvalues ₁ = -2, A2 = 0.25 A3 = 1.6 with corresponding eigenvectors 0 Го Consider the difference equation With initial condition x0 = 517 V1 Xk+1 = Mxx 2 Write the initial condition as a linear combination of the eigenvectors of M. That is, write x0 = c1V1 + C2V2 + C3V3 = In general, X = Specifically, x4 = Vi+ ) Vi+ For large k, xk ≈ k V3 V2+ ။ 2 3 23 k ) V2 V2+ V3 ) V3

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