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Eigenvalues & Eigenvectorshard
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The characteristic polynomial of A=(52−4−1)A = \begin{pmatrix}5 & 2 \\ -4 & -1\end{pmatrix}A=(5−4​2−1​) is (λ−1)(λ−3)(\lambda-1)(\lambda-3)(λ−1)(λ−3). Find the eigenvalues and verify using tr(A)\text{tr}(A)tr(A) and det⁡(A)\det(A)det(A).