It's a very basic question. If I'm not wrong the Lie theorem says that any solvable sub-algebra of $\mathfrak{gl}\left(V\right)$ over complex numbers with $V$ finite dimensional is isomorphic to a sub-algebra of the algebra of upper triangular matrices $\mathfrak{b}(n)$ to some $n$.
Isn't Ado theorem + Lie theorem implying that every solvable finitedimensional Lie algebra is isomorphic to a sub-algebra of $\mathfrak{b}(n)$?
I suppose that should be the case, but I couldn't find an explicit reference and wanted to be sure that I'm not missing something...