Lost in the Array of Operations When Multiplying Matrices

Date: 03/30/2010 at 11:57:58
From: Maria
Subject: getting lost in the array of operations when solving matrix

When I'm solving matrices, I always have the same problem. Theoretically,
I know how to solve them, but I always come up with a wrong answer. Even
worse, if I repeat the same exercise, in the end I get something wrong and
different from the previous mistake!

I've concluded I get confused with so many operations to apply. I
figured it could be a problem of concentration, but I'm not able to solve
this on my own. I've tried coffee, gotten more hours of sleep, did my best
to stay focused on the exercise....

Could you please help me?

Thank you :)
Maria

Date: 03/30/2010 at 13:04:00
From: Doctor Ian
Subject: Re: getting lost in the array of operations when solving matrix

Hi Maria,

Can you give me an example of a matrix problem you want to solve? 

Often the key to dealing with lots of operations is to group them in a way
that makes it easier to keep track of what's going on.

For example, if you want to multiply two matrices, 

   _       _   _  _     _  _
  |  2 3 4  | |  2 |   |  ? |
  |         | |    |   |    |
  |  7 6 5  | |  3 | = |  ? |
  |         | |    |   |    |
  |_ 3 6 9 _| |_ 5_|   |_ ?_|

... you can try to remember all the individual operations -- or you can
think of it this way:

   _       _   _  _     _                     _
  |  2 3 4  | |  2 |   |  (2 3 4) dot (2 3 5)  |
  |         | |    |   |                       |
  |  7 6 5  | |  3 | = |  (7 6 5) dot (2 3 5)  |
  |         | |    |   |                       |
  |_ 3 6 9 _| |_ 5_|   |_ (3 6 9) dot (2 3 5) _|

Now you know everything's in the right place, so you can focus on the dot
products:

   _       _   _  _     _                  _
  |  2 3 4  | |  2 |   |  2*2 + 3*3 + 4*5   |
  |         | |    |   |                    |
  |  7 6 5  | |  3 | = |  7*2 + 6*3 + 5*5   |
  |         | |    |   |                    |
  |_ 3 6 9 _| |_ 5_|   |_ 3*2 + 6*3 + 9*5  _|

And you can do the same thing for matrices with other shapes: every
element of the product is the dot product of a row of the first matrix and
a column of the second.

Even if this isn't exactly the kind of problem you're trying to solve, can
you see what I'm getting at? Does it make sense?

- Doctor Ian, The Math Forum
  http://mathforum.org/dr.math/ 

Date: 03/31/2010 at 09:36:27
From: Maria
Subject: Thank you (getting lost in the array of operations when solving matrix)

Hi!

Thank you for answering so quickly! I dind't answer sooner because I
wanted to try your suggestion first.

... and it worked!!!! :) I got many more exercises right! Thank you so
much.

I'd also like to say that I really admire the fact that you volunteer and
you give a part of your time to help people like me in this kind of
subjects. There are people who volunteer in Africa and there are others
like you, who volunteer in their daily life :P