MT Exercise-11-정태일

Exercise 11) Find a substitution  $\rm\bold x=\it Q\rm\bold y$ that diagonalizes each of the following quadratic forms, where $Q$ is orthogonal. Also, classify the form as positive definite, positive semidefinite, and so on.

1)  $q(\rm\bold x)=\it 2x^2+6xy+2y^2$

2)  $q(\rm\bold x)=\it x^2+y^2+z^2+2(xy+xz+yz)$

Sol)

1)

2)