For a 3x3 matrix, how to find the eigenvalues without using its characteristic equation, if one of the eigenvalues is given. Suppose 2 is an eigenvalue of the matrix A, and find the others without using its characteristic equation $$A = \begin{bmatrix}3&-1&1\\-1&5&-1\\1&-1&3\end{bmatrix}$$
2026-03-26 21:12:22.1774559542
Find the eigen value of a matrix without using the characteristic eqution
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Hint- Let $\alpha$ and $\beta$ are the other two eigenvalues. Then
$\implies \alpha+\beta=9$
$\implies \alpha\beta=18$