3. For the matrix $A = \begin{bmatrix} 1 & 2 & -1 \\ 2 & 1 & -1 \\ 3 & 0 & -1 \end{bmatrix}$ find the eigenvalues and the eigenvectors.
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det(A-λI) = det(3-λ 0; 0 2-λ) = (3-λ)(2-λ) - 0 = 6 - 5λ + λ^2 Setting this equal to zero and solving for λ, we get: λ^2 - 5λ + 6 = 0 (λ-2)(λ-3) = 0 Therefore, the eigenvalues are λ1 = 2 and λ2 = 3. Show more…
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