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))#