User:Komma

User page/sandbox.

Testing.

$$\begin{vmatrix} a_{11} & a_{12} & a_{13}\\a_{21} & a_{22} & a_{23}\\a_{31} & a_{32} & a_{33}\end{vmatrix} = a_{11} a_{22} a_{33} + a_{12} a_{23} a_{31} + a_{13} a_{21} a_{32} - a_{11} a_{23} a_{32} - a_{12} a_{21} a_{33} - a_{13} a_{22} a_{31}$$

$$\begin{matrix} a_{11} & a_{12} & a_{13} & a_{11} & a_{12} & a_{13} & a_{11} & a_{12} & a_{13}\\a_{21} & a_{22} & a_{23} & a_{21} & a_{22} & a_{23} & a_{21} & a_{22} & a_{23}\\a_{31} & a_{32} & a_{33} & a_{31} & a_{32} & a_{33} & a_{31} & a_{32} & a_{33}\end{matrix}$$

$$\rho = \frac{n_1(\rho_1^2 + \bar{x}_1^2) + n_2(\rho_2^2 + \bar{x}_2^2)}{n_1 + n_2}$$