Math Is Fun Forum

Bob

Administrator

Registered: 2010-06-20

Posts: 10,619

multiplying matrices

hi 666bro,

You've asked about multiplying matrices.

I'll use an example to show how it works.

John, Mary and Paul are buying sweets. 
John buys 2 choc bars, 1 fruity sweet, no chews and 3 lollipops.
Mary buys 4 choc bars, no fruity sweets, 1 chew and 1 lollipop.
Paul buys no choc bars, 1 fruity sweet, 2 chews and 1 lollipop.

We can summarise that using a 3 by 4 matrix.

Here are the prices:
choc bars 15p; fruity sweets 7p; chews 2p; lollipops 5p.

We can put that in a 4 by 1 matrix.

So now let's find out how much each child has to pay. We can multiply the two matrices.  The number of columns in the first must match the number of rows in the second.  The answer matrix has the same rows as the first and the same columns as the second.  ie 3 by 4 times 4 by 1 gives a 3 by 1 result.

Each row of the first is combined with each column of the second by multiplying the first elements, then adding the second elements multiplied, then adding the third elements multiplied and so on.

So if the Nth row of the first consists of {a b c d e} and the Mth  column of the second consists of {p q r s t}, then the Nth row Mth column value of the product is ap + bq + cr + ds + et

Hope that helps,

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

mathdrop

Member

Registered: 2022-03-07

Posts: 75

Re: multiplying matrices

how would be the procedure again,
if the second matrix would have multiple, lets say 3, columns
and what would that mean ?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,619

Re: multiplying matrices

Just treat, say, 4 by 6 matrix as 6 separate 4 by 1s and do the multiplication of each column like that.

So for example if you have a 3 by 4 to multiply a 4 by 6 you treat the 6 columns like in the above post and then re-assemble the answer. It will be a 3 by 6 matrix.

Bob

ps. You may be able to help another member who is having difficulty making a new post. He keeps adding his new posts to existing threads.  When you view the forum on a phone can you see the post numbers?  And if you switch to the help index can you see the 'make a new post' option?

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob