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

Row Matrix  ×  Col. Matrix   =   Scalar

1 × 2             2 × 1      =   1 × 1

Answer:

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:

dot product

It might look slightly odd to regard a scalar (a real number) as a "1 × 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:

dot product

QUESTION 5:

Here is another example, with the result left blank:

dot product

Compute the result.


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