Linear Algebra Quiz
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EIGENVALUES & EIGENVECTORS
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For a discrete system x⃗k+1=Ax⃗k\vec{x}_{k+1} = A\vec{x}_k with A=(4−211)A = \begin{pmatrix} 4 & -2 \\ 1 & 1 \end{pmatrix}, and a generic initial vector x⃗0\vec{x}_0 not in an eigenspace, the vector x⃗k\vec{x}_k will align with a specific direction as k→∞k \to \infty. What is this long-term direction?
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