Question

Question #48675

Answer 1

I will explain how to multiply matrices. (If that's not what you meant by the multiplication law, I apologize for misunderstanding.)

Explanation:

There is some information on Multiplication of Matrices here on Socratic.

I think of it as a process that is easier to explain in person, but I'll do my best here.

Let's go through an example:

`((1, 2),(3, 4)) ((3, 5),(7, 11))`

Find the first row of the product

Take the first row of `((1, 2),(3, 4))`, and make it vertical in front of `((3, 5),(7, 11))`. (We'll do the same for the second row in a minute.)

It looks like:

`{: (1),(2) :}((3, 5),(7, 11))`

Now multiply times the first column and add to get the first number in the first row of the answer:
`{:(1 xx 3),(2 xx 7) :}={:(3),(14) :}` now add to get `17`

The product starts with:
`((17,"-"),("-","-"))`

Next multiply times the second column and add to get the second number in the first row of the answer:
`{:(1 xx 5),(2 xx 11) :}={:(5),(22) :}` now add to get `27`

The first row of the product is: `((17,27))`

A this point we know that the product looks like:

`((1, 2),(3, 4)) ((3, 5),(7, 11)) = ((17,27),("-","-"))`

Find the second row of the product
Find the second row of the product by the same process using the second row of `((1, 2),(3, 4))`

`{: (3),(4) :} ((3, 5),(7, 11))` to get: `9+28 = 37` and `15+44 = 59`

The second row of the product is: `((37,59))`

Write the answer

`((1, 2),(3, 4)) ((3, 5),(7, 11)) = ((17,27),(37,59))`