How can I use Bordered Hessians to determine the sign properties (definiteness) of the following constrained quadratic form:
$$Q(x_1, x_2, x_3) = x^2_1 + 2x^2_2 − 2x^2_3 + 4x_1x_2 − 2x_2x_3$$
subject to the constraints $2x_1+x_2+x_3 = 0$ and $x_1−x_2−x_3 = 0$? I need to then verify the result by eliminating two of the variables using the constraints, and determine the sign property of the reduced quadratic form.
Has anyone got any idea how to approach a question like this?