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Obtain a spectral decomposition for the symmetric matrix A = [0 2 2, 2 0 2,...

Obtain a spectral decomposition for the symmetric matrix A = [0 2 2, 2 0 2, 2 2 0] (that means the first row is 022, then below that 202, etc.) , whose characteristic polynomial is −(λ + 2)^2 (λ − 4) If you could provide a step-by-step way to solve this I'd greatly appreciate it.

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