Let M be a 2 x 2 matrix with eigenvalues ₁ = -0.8, 2 = 1 with corresponding eigenvectors Consider the difference equation with initial condition X = V₁ = = [22] [22] V2 Xk+1 = MX Mxk Write the initial condition as a linear combination of the eigenvectors of M. That is, write x0 =C1V1 + C2V2 = In general, X = V1+| V2 )ε vi+ k Specifically, X2 = For large k, xk → k V2

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