1.8.2 Quadratic forms

Problem: At what values of \( \lambda \) the following quadratic form is positive definite: \[ f=5 x_{1}^{2}+x_{2}^{2}+\lambda x_{3}^{2}+4 x_{1} x_{2}-2 x_{1} x_{3}-2 x_{2} x_{3} . \]