How do I do multiplication of matrices?

1 Answer
Sep 9, 2015

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))