Change PDE in 3 variables to standard (canonical) form

Question

I know how to change a 2 variables PDE like $$u_{xx} + 2u_{xy} + u_{yy} +u_x + u_y = 0$$ to a standard(canonical) form.

But how we gonna do with a 3 variables PDE ? Such as:

$$3u_{xx} − 2u_{xy} + 2u_{yy} − 2u_{yz} + 3u_{zz} + 5u_y − u_x + 10 u = 0$$

I know it has something to do with the matrix, but any friend could please show me the process?

Thanks in advance