Classify the quadratic then make a change of variable x py

Question

Question: Classify the quadratic then make a change of variable, x = Py, that transforms the quadratic form into one with no cross-product term. Write the new quadratic form. Construct P using the methods.

[M] 11x₁² - x₂² - 12x₁x₂ - 12x₁x₃ - 12x₁x₄ - 2x₃x₄