Question

If you multiply a $2\times 2$ matrix and a $2\times 1$ matrix the product is a $2\times 1$ matrix?

• A. True
• B. False

Answer 1

The correct option is A True

Yes, it will 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):
$2\times 2$ and $2\times 1$
So the result will be a $2\times 1$.
The internal ones $2$ and $2$ tell you if the multiplication is possible (when they are equal) or not (when they are different).
For example:
$\left(\begin{array}{cc}2& 1\\ 3& 2\end{array}\right)\times \left(\begin{array}{c}1\\ 2\end{array}\right)=\left(\begin{array}{c}2.1+1.2\\ 3.1+2.2\end{array}\right)={\left(\begin{array}{c}4\\ 7\end{array}\right)}_{2\times 1}$