写出下列二次型的矩阵，并求它们的秩.
(1) $f_1=3 x_1^2+2 x_2^2-x_3^2+2 x_1 x_2-4 x_2 x_3$.
(2) $f_2=x_1^2-2 x_1 x_3$.
(3) $f_4=\left[\begin{array}{lll}x_1 & x_2 & x_3\end{array}\right]\left[\begin{array}{lll}1 & 4 & 3 \\ 2 & 2 & 6 \\ 1 & 0 & 3\end{array}\right]\left[\begin{array}{l}x_1 \\ x_2 \\ x_3\end{array}\right]$.