2*2 x 2*1 is doable because the 2 middle numbers are the same. and the resultant matrix will be 2*1 (the outer numbers.
$$\begin{pmatrix}
1 &2 \\
3 & 4
\end{pmatrix}
\times %
\begin{pmatrix}
5 \\
6
\end{pmatrix}
=%
\begin{pmatrix}
1*5+2*6 & \\
3*5+4*6 &
\end{pmatrix}
=%
\begin{pmatrix}
17 \\
39
\end{pmatrix}$$
2*2 x 2*1 is doable because the 2 middle numbers are the same. and the resultant matrix will be 2*1 (the outer numbers.
$$\begin{pmatrix}
1 &2 \\
3 & 4
\end{pmatrix}
\times %
\begin{pmatrix}
5 \\
6
\end{pmatrix}
=%
\begin{pmatrix}
1*5+2*6 & \\
3*5+4*6 &
\end{pmatrix}
=%
\begin{pmatrix}
17 \\
39
\end{pmatrix}$$