HELP!!! Multiplying MATRICES!

[rollerz]

Hey guys,

I'm a bit confused as to how the mutiplication of matrices actually works, Im okay with ones of the same dimensions but once you get different dimensions going I get really confused...

Any help would be really great!
Thanks guys!

[the.watchman]

Ok, so first start with the dimensions:

When multiplying an m x n matrix by a p x q matrix, the result is defined IF n = p
The dimensions of the final will be m x q

I've just realised I can't really draw matrices here very well, so I'll hand part 2 over to someone else

[rollerz]

Hold on, so what you're trying to say is that n has to equal p for the matrix to actually be solveable?
So if you were multipying a matrix of 5x6 by a matrix of 2x6 it wouldnt work, but if it was a 5x6 by a 6x2 it would???
Thanks for replying so fast.

[the.watchman]

Hold on, so what you're trying to say is that n has to equal p for the matrix to actually be solveable?
So if you were multipying a matrix of 5x6 by a matrix of 2x6 it wouldnt work, but if it was a 5x6 by a 6x2 it would???
Thanks for replying so fast.

Yep, thats correct
I wish I could continue, but it would take WAY too long

[simonhu81292]

yep... the watchman is pretty fast
i was about to answer it
but then refreshed
you've already done it

[rollerz]

Ok, well that makes a bit more sense, thanks for the help!

[the.watchman]

No prob, remember that if the dimensions suggest that there is no result to a particular product, then just answer the question with 'undefined' or do what the TI-Nspire says: "Dimension error"

If you actually think about the method, you'll understand why it can't work

[stonecold]

Yeah, if you are multiplying matrices AB, then they must have dimensions m x n and n x p respectively, and the resultant matrix will have dimensions m x p.

This is the way I remember it.  Number of columns in the first matrix must equal the number of rows in the second matrix.

[simonhu81292]

([1][3])         ([2])
([2][4]) times ([1])
so 2 by 2 time 2 by 1
1 X 2= 2  and 3 X 1= 3 add them to get your answer for top which it's 5
then the bottom 2 X 2=4 and 4 X 1=4 .. 4+4= 8
so the answer would be ([5])
                                 ([8])
the best i could do
 

[the.watchman]

Good on you simonhu!

Basically start top left on the left matrix and multiply it by the top left on the right matrix.
Then, move along the row (for left matrix) or column (for right matrix) to continue working for that element.The row/column should correspond to the position on the resulting matrix.

I hope that made some sort of sense

[simonhu81292]

yeah...
i'll let the.watchman take over..lol
pro at explaining!!

[the.watchman]

LETS GO WACKY!!!

For the matrix equation,

(little 'c' indicating element in C; 'i' being any row number; and 'j' being any column number)

Now does this make sense?!?!

[stonecold]

lol, i'll stick to my lame further notation thanks

[the.watchman]

LOL, don't worry it's not important
But if you ever have trouble, just plug the numbers in to get the answer

[QuantumJG]

Multiplication is a pretty simple task.

x =

Now for matrix sizes. Let's say we have two matrices (A & B). Now A is an a x b matrix & B is an c x d matrix. Now firstly let's look at A x B.

A x B will produce a a x d matrix that exists iff b = c & B x A will produce an c x b matrix that exists iff d = a.

For example:

x = =