The first matrix has dimensions 4 down by 6 across.
That's a 4x6 matrix.
The second matrix has dimensions 6 down by 4 across.
That's a 6x4 matrix.
Write 4x6 6x4
The two (blue) inner dimensions are both 6. They must be the same
in order for the matrices to even be multipliable. If they weren't the
same, the multiplication would not be defined. Since they are both
6, they can be multiplied. The product matrix will have the two outer
(red) dimensions. They are both 4, so the product matrix will be a
4x4 matrix.
Set the product equal to a 4x4 matrix of blanks to
fill in.
I won't go through all 16 blanks. I will only tell you how to fill in
three of them at random. Then you will know how to do all the rest.
---
Let's fill in the blank which is in row 3 and column 2:
Take row 3 from the first matrix:
and column 2 of the second matrix:
Multiply corresponding elements then add them all:
=
So put a in the blank in row 3 and column 2:
---
Next let's fill in the blank in the upper right hand corner.
That is the blank in row 1 and in column 4:
Take row 1 from the first matrix:
and column 4 from the second matrix:
Multiply corresponding elements then add them all:
=
So put a in the blank in row 1 and column 4:
----
One more!
Let's fill in the blank in row 2 and column 1:
Take row 2 from the first matrix:
and column 1 of the second matrix:
Multiply corresponding elements then add them all:
=
So put a in the blank in row 2 and column 1:
Do you see how to do it now? To fill in any blank in the
product matrix, you decide which row and column the blank
is in which you want to fill, then get the corresponding
row from the first matrix, and the corresponding column
from the second matrix, then multiply corresponding elements
and add them. You can fill them in in any order you choose.
When you fill in the rest of the blanks you should have this:
Edwin
