It will prove convenient to express the dot product in a form where its left input is a row vector, and its right input is a column vector.

So we would write:

\\[

\begin{bmatrix}

1 & 2

\end{bmatrix}

\cdot

\begin{bmatrix}

10 \\\\

20

\end{bmatrix}

=

1 \cdot 10 + 2 \cdot 20 =50

\\]

So we would write:

\\[

\begin{bmatrix}

1 & 2

\end{bmatrix}

\cdot

\begin{bmatrix}

10 \\\\

20

\end{bmatrix}

=

1 \cdot 10 + 2 \cdot 20 =50

\\]