If you multiply a 2x2 matrix and a 2x1 matrix the product is a 2x1 matrix?

Jul 17, 2015

Yes, it wll give you a $2 \times 1$ matrix!

Explanation:

When you consider the order of the matrices involved in a multiplication you look at the digits at the extremes to "see" the order of the result.
In this case (red digits):
$\textcolor{red}{2} \times 2$ and $2 \times \textcolor{red}{1}$
So the result will be a $2 \times 1$.

The internal ones $2 \mathmr{and} 2$ tell you if the multiplication is possible (when they are equal) or not (when they are different).

For example:
$\left(\begin{matrix}2 & 1 \\ 3 & 2\end{matrix}\right) \times \left(\begin{matrix}1 \\ 2\end{matrix}\right) = \left(\begin{matrix}2 \cdot 1 + 1 \cdot 2 \\ 3 \cdot 1 + 2 \cdot 2\end{matrix}\right) = {\left(\begin{matrix}4 \\ 7\end{matrix}\right)}_{2 \times 1}$