Chapter 7 - Eigenvalues and Eigenvectors - 7.4 Applications of Eigenvalues and Eigenvectors - 7.4 Exercises - Page 384: 45

$\begin{bmatrix} 0& 5 \\ 5&-10\\ \end{bmatrix} $

The expression $ax^2+bxy+cy^2=0$ is associated with the equation $ax^2+bxy+cy^2+dx+ey+f=0$. Then A is the quadratic form given by $\begin{bmatrix} a& b/2 \\ b/2&c\\ \end{bmatrix} $. Here $a=0,b=10,c=-10$; hence the matrix of the quadratic form is: $\begin{bmatrix} 0& 5 \\ 5&-10\\ \end{bmatrix} $