Algebra 2 More Matrix Operations
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I was a Teenage Matrix
More Matrix Operations

 

 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

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