



Here
are a few more general Matrix techniques



you
should probably see ... 





Matrix
Addition 





You can
add two matrices together IF they are the same size. 


To do
it, 


just add
together the numbers that are in the same space in each matrix. 


The new
matrix that you get will be the same size as the originals ... 





Example: 








Matrix
subtraction works just like matrix addition ... 





Example: 








Matrix
multiplication, however, is a lot different. 


The two
matrices DO NOT have to be the same size. 


We do not
always multiply numbers together 


that are
in the same place in the matrix. 





Here's
how it works. 


The lines
of numbers going from left to right in the matrix 


are
called rows. 


The lines
of numbers going from top to bottom in a matrix 


are
called columns. 








There is
one rule about matrix size and multiplication. 


The
number of columns in the first matrix 


must
equal the number of rows in the second matrix. 





Example: 


Say you
want to multiply these two matrices: 











The first
matrix has 3 columns. 


The
second matrix has 3 rows. 


So we can
do it. 





The first
step is to multiply the numbers in Row 1 of the first matrix 


by the
numbers in column 1 of the second matrix 


then add
those number together 


and put
them in the first space in the column 1 in an output matrix ... 











Then
multiply the numbers in the Row 2 of the first matrix 


by the
numbers in COLUMN 1 of the second matrix 


then add
those numbers together 


and put
them in the second space in column 1 of the output matrix. 











Now
multiply the Row 3 of the first matrix 


by COLUMN
1 of the second matrix 


then add
those numbers together 


and put
them in the third space in column 1 of the output matrix. 











Now we do
the whole thing over using the second column of the second matrix
... 











So: 











The
product matrix we wind up with 


will have
the same number of rows as the first matrix 


and the
same number of columns as the second matrix. 





copyright 2005 Bruce Kirkpatrick 
