(a) Find a 3 x 3 symmetric matrix, A, whose eigenvalues are A₁ = -4, A₂ = 2, A3 = 6 and for which the corresponding eigenvectors are v₁ = (0, 1, -1), v2 = (1, 0, 0), v3 = (0, 1, 1) A = (b) Is there a 3 x 3 symmetric matrix with eigenvalues A₁ = -4, A₂ = 2, A3 = 6 and for which the corresponding eigenvectors are v₁ = (0, 1,-1), v₂ = (1, 0, 0), v3 = (1, 1, 1).

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