Matrix

A matrix isn't just a Hollywood movie.  It is an ordered rectangular array of numbers or functions into rows and columns.  The numbers or functions are called the elements or entries of the matrix.
We denote matrices by capital letters.
The following are some examples for matrices.
Klan has 20 shirts and 14 pants
Alan has 12 shirts and 7 pants
Chris has 8 shirts and 8 pants

Now we can arrange this in a tabular form as follows
                            Shirts                    Pants
         Klan                20                        14
         Alan                12                         7
        Chris                 8                          8

The horizontal lines of elements are said to constitute, rows of the matrix and the vertical lines of elements are said to constitute, columns of the matrix.
Given below some matrices, write the number of rows and columns for each matrix.

Number of rows of A = 3   No. of rows of B = 3        No. of rows of C = 2
No. of columns of A = 2     No. of columns of B = 1   No. of columns of C = 3

Order of a Matrix

If a matrix has ‘m’ rows and ‘n’ columns then its order is m x n (read it as m by n)
Generally we denote A = [a_ij] _{m x n} to indicate that A is a matrix of order m x n
From the above examples we can say,
Order of A = 3 x 2
Order of B = 3 x 1
Order of C = 2 x 3
In general a_ij means the element which belongs to i^th row and j^th column
For example,
                          
In the matrix  , write
                  
i) The order of the matrix, 
ii) The number of elements
iii) Write the elements a₁₃, a₂₁, a₃₃, a₂₄, a₂₃
Solution: i) Order of the matrix A is 3 x 4
ii) Number of elements =12
iii) a₁₃ = 19, a₂₁ = 35, a₃₃ = -5, a₂₄ = 12 and a₂₃ = 5/2
Example: If a matrix has 18 elements, what are the possible orders it can have?
Solution:  The possible orders are 1 x 18, 2 x 9, 3 x 6, 6 x 3, 9 x 2, 18 x 1
                                       

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Reference Links:

• http://en.wikipedia.org/wiki/Matrix_(mathematics)
• http://en.wikipedia.org/wiki/Row_and_column_spaces
• http://www.mathreference.com/la-mpoly,order.html