Question: Does there exist a 3 à 3 symmetric matrix with eigenvalues λ1 = -1, λ2 = 3, λ3 = 7 and corresponding eigenvectors If so,

Does there exist a 3 × 3 symmetric matrix with eigenvalues λ1 = -1, λ2 = 3, λ3 = 7 and corresponding eigenvectors
Does there exist a 3 × 3 symmetric matrix with

If so, find such a matrix; if not, explain why not.

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