Dot Product as Matrix Multiplication
Just by looking at the dimensions, it seems that this can be done. Of course, that is not a proof that it can be done, but it is a strong hint. Here is an example:
It might look slightly odd to regard a scalar (a real number) as a "1 x 1" object, but doing that keeps things consistent. Notice that this example looks like a dot product. In fact, it is. Knowing that, you know how the product is formed:
Here is another example, with the result left blank:
