For the following Quadratic Form :
$$Q(X)=x_1^2-6x_1x_2+9x_2^2$$
Represent the quadratic form using a matrix
I know that $B(u,v)=\frac{1}{4}[Q(u+v)-Q(u-v)]$ iff $B$ is symmetric
How can I use this formula to find $B$?
Or I can use the fact that $ax_1^2+bx_2^2+2cx_1x_2+dx_1+ex_2+f=0$ can be written as
$\begin{pmatrix} x_1 & x_2 \end{pmatrix}\begin{pmatrix} a & c\\ c & b \end{pmatrix}\begin{pmatrix} x_1 \\ x_2 \end{pmatrix}+\begin{pmatrix} d & e \end{pmatrix}\begin{pmatrix} x_1 \\ x_2 \end{pmatrix}+f=0$
So the matrix is just \begin{pmatrix} 1 & -3\\ -3 & 9 \end{pmatrix}?