A population redistributes each year by matrix $A$, and $v$ is an eigenvector with eigenvalue $\lambda = 2$. If the population starts at $v$ with total 100, what is the total after 3 years? Set the slider to your answer.

800 (answers within ±24 count)

On an eigenvector, matrix dynamics collapse into scalar dynamics: $2^{3} = 8$-fold growth, so 800. This is why eigenvalues govern long-run behaviour, whichever eigenvalue is largest eventually dominates any starting mix.