matrix

							MATRIX: A rectangular
arrangement of                  This order of this matrix
numbers in rows and             is a 2 x 3.
columns.
                                columns
The ORDER of a matrix
is the number of the
rows and columns.                6 2  1
The ENTRIES are the
                                 2 0 5 
                                        
numbers in the matrix.
                         rows
8     1      3               (or square   9    5 7          0
0     0       2
                         3x3
                                matrix)
                                                1x4
                                                          (Also called a
                                                          column matrix)
 10
      4       3
                 

 2   0      4      6     3
1                                                             9
      1     5 9         8
                                    3x5                      7 
7                         6                                  
      3      2      7                                       0
                                                               
                                                              6
 1         1      2x2
                           (or square
 0                       matrix)                           4x1

          2                                           (Also called a
                                                        row matrix)
To add two matrices, they must have the same
order. To add, you simply add corresponding
entries.
  5     3   2    1     5  (2)  3  1 
  3                         33            
        4  3
                    0 
                        
                                       40 
  0
        7   4
                    3
                             04
                                      7  (3)
                                               

                              3     2
                             0
                                    4 
                                       
                              4
                                    4 
                                       
          8 0 1 3   1 7                     5  2
          5 4 2 9    5 3                    3  2
                                                   


=
            8  (1)

              5 5
                            07
                            4 3
                                   1 5
                                   2 3
                                               3 2
                                              9  (2)   
    =
            0
              7
                    7
                        7    4
                             5
                                   5
                                   7
                                          
 To subtract two matrices, they must have the same
 order. You simply subtract corresponding entries.

 9 2 4   4 0 7   9 4        20      47 
 5 0 6    1 5  4                            
                     5 1     05    6  (4)
 1 3 8   2 3 2  1  (2)
                               33      82  
                             5     2      3
                             4
                                  5        
                                           10 
                             3
                                    0      6 
                                              
        2       4      3 0     1         8
        8       0            3 1
                         7                 
                                             1
        
        1
                5       0   4 2
                                           7
                                              


=
        2-0
        8-3
        1-(-4)
                 -4-1
                 0-(-1) -7-1
                  5-2
                         3-8


                          0-7
                                
                                =
                                     2 -5 -5
                                     5 1 -8
                                     5   3   -7
                                                  
 In matrix algebra, a real number is often called a SCALAR.
 To multiply a matrix by a scalar, you multiply each entry in
 the matrix by that scalar.


  2       0    4(2)                   4(0) 
4              
             1                                 
  4               4(4)                   4(1) 
                       8             0 
                                       
                       16             4
    1         2   4      5 
 2 
    0             6          
              3            8 

     1 4               2  5 
 2 
     06
                                  
                                 
                      3  (8) 

-2
          -3 3
                   
                                       
            6 -5


    -2(-3) -2(3)
      -2(6)    -2(-5)
                           
                                 6 -6
                                -12 10
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