1.8.7 Quadratic Forms

Condition: a quadratic form is set \ (\ varphi \ left (x_ {1}, x_ {2}, x_ {3} \ right) \). 1) bring it to the canonical appearance by the Lagrange method by writing out the appropriate transformation of the variables. 2) bring it to the canonical appearance of an orthogonal transformation. 3) check the law of inertia of quadratic forms on examples of transformations obtained in previous paragraphs 1) -2). 4) What surface is set by the equation \ (\ varphi \ left (x_ {1}, x_ {2}, x_ {3} \ right) = 1 \)? \ (\ varphi \ left (x_ {1}, x_ {2}, x_ {3} \ right) = 2 x_ {1}^{2} +9 x_ {2} +2 x_ {3} {2} -4 x_ {1} x_ {2 x_ {2} x_ {3} \).