Matrix Multiplication

Hi Brooke,

Let's look at two matrices like

| a b | | u v w |
| c d | | x y z |
| e f |

The product of the matrices will look like

| a b | | u v w | | ? ? ? |
| c d | * | x y z | = | ? ? ? |
| e f | | ? ? ? |

Each '? will be replaced by the dot product of a row of the first
matrix, and a column of the second. For example,

| a b | | u v w | | ? ? ? |
| c d | * | x y z | = | ? ? ? |
| e f | | ? _ ? |
^
|
element in 3rd row, 2nd column
is dot product of 3rd row of first matrix
and 2nd column of second matrix

Note that this is _why_ the number of columns in the second matrix has
to be the same as the number of rows in the first.

What is a dot product? Note that each row of the first matrix has the
same number of elements as each column of the second matrix. This
isn't an accident. It's a requirement. To find the dot product of
the row (e,f) and the column (v,y), we multiply the corresponding
elements and add the products:

(e,f).(v,y) = ev + fy

So this is what goes in the result matrix:

| a b | | u v w | | ? ? ? |
| c d | * | x y z | = | ? ? ? |
| e f | | ? ev+fy ? |

Is this enough to get started?