Question

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

Answer 1

Yes, it wll give you a `2xx1` 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):
`color(red)(2)xx2` and `2xxcolor(red)(1)`
So the result will be a `2xx1`.

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:
`((2,1),(3,2))xx((1),(2))=((2*1+1*2),(3*1+2*2))=((4),(7))_(2xx1)`