Question

Diagonalize the matrix and find the trace (T_r = λ₁ + λ₂ + λ₃)

|(6, -2, 2), (-2, 3, - 1), (2, -1, 3)|

Answer 1

The two vectors are X₁ = (1, 1, −1) and X₂ = (0, 1, 1) . The third vector can be obtained in a similar fashion. It can be chosen as X₃ = (2, −1, 1) . The three column vectors can be normalized and arranged in the form of a matrix. The matrix A is diagnalized by the similarity transformation.