It can be shown that the eigenvalues of a are 3 9 and 15

Question

Question: Let A be the matrix of the quadratic form

9x₁² + 7x₂² + 11x₃² - 8x₁x₂ + 8x₁x₃

It can be shown that the eigenvalues of A are 3, 9, and 15. Find an orthogonal matrix P such that the change of variable x = Py transforms x TAx into a quadratic form with no cross product term. Give P and the new quadratic form.