Linear Dynamical Systems

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Example: Linear Dynamical Systems

Consider the linear dynamical system given by
xn+1=2xn+ynyn+1=xn+2yn\begin{array}{l}x_{n+1}=2x_n+y_n\\y_{n+1}=x_n+2y_n\end{array}
with initial conditions x0=1x_0 = 1, y0=2y_0 = 2. Find solutions to this system for general nn and for n=3n = 3.
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