\edit2
final answer:
\begin{align*}
\begin{vmatrix} 1 \\ 2 \end{vmatrix} &\begin{vmatrix} 1 & 2 & 3 \\ 3 & 4 & 5 \end{vmatrix} \\[6px]
&\begin{vmatrix} 2 & 3 & 4 \end{vmatrix}
\end{align*}
does exactly what you want, read below for more info about placement and such. The "&" sign is used to align in general. Forgot the first line had 2 matrices but now you have it :).
info on spacing and such
\begin{align*}
&\begin{pmatrix} 1 & 2 & 3 \ 3 & 4 & 5 \end{pmatrix} \[6px]
&\hspace{2px}\begin{pmatrix} 2 & 3 & 4 \end{pmatrix}
\end{align*}
would do the job. For some strange reason the align gave errors when leaving out the first "&" symbol and it gave a 2px offset. I figured you wanted some space between the two if not leave the [6px]. You can always use \hspace{amount of whitespace} to place your second matrix in the place you want. This can be given in pt's, px's (which i did) etc.
//edit
Hm I notice the \hspace{} is actually not needed, but can be used in case of pmatrix. What happens is that the pmatrix brackets give a biased image of the matrices. When using vmatrix like:
\begin{align*}
&\begin{vmatrix} 1 & 2 & 3 \\ 3 & 4 & 5 \end{vmatrix} \\[6px]
&\begin{vmatrix} 2 & 3 & 4 \end{vmatrix}
\end{align*}
It all goes well :). So basically, probably the easiest way to fix it is either use other brackets to make it look good or use the \hspace to align as you like it.