Do you think that it is possible to form a product that looks like this:

Row Matrix  x  Col. Matrix   =   Scalar

1 x 2             2 x 1      =   1 x 1

A good answer might be:

Yes. It looks like it can be done.

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:


Compute the result.