91Ó°ÊÓ

Classify the quadratic forms in Exercises \(9-18 .\) Then make a change of variable, \(\mathbf{x}=P \mathbf{y},\) that transforms the quadratic form into one with no cross-product term. Write the new quadratic form. Construct \(P\) using the methods of Section \(7.1 .\) $$ 4 x_{1}^{2}-4 x_{1} x_{2}+4 x_{2}^{2} $$

Find the SVD of \(A=\left[\begin{array}{ccc}{3} & {2} & {2} \\ {2} & {3} & {-2}\end{array}\right]\left[\text { Hint: Work with } A^{T} .\right]\)