Find the real symmetric 3 x 3 matrix with eigenvalues $\lambda_1 = -1, \lambda_2 = -4, \lambda_3 = -4$ and corresponding mutually orthogonal eigenvectors
$v_1 = \begin{bmatrix} 4 \\ 5 \\ -1 \end{bmatrix}$, $v_2 = \begin{bmatrix} 3 \\ -3 \\ -3 \end{bmatrix}$, $v_3 = \begin{bmatrix} -2 \\ 1 \\ -3 \end{bmatrix}$
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