Ononot — A population model has \mathbf{x}{n+1} = A\mathbf{x}n where

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Eigenvalues & Eigenvectorseasy

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A population model has $\mathbf{x}_{n+1} = A\mathbf{x}_n$ where $A = \begin{pmatrix} 0.5 & 2 \\ 0.5 & 0 \end{pmatrix}$ has dominant eigenvalue $\lambda_1 \approx 1.207 > 1$ . What is the long-term behavior?