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The entries in the rows represent number of oranges and apples bought by Ganga, Hemant and Gargi respectively.
                 Or in another form as:
                                                            12  10   5 −Row 1
                                                                       
                                                                        
                                                            5   7    2 −Row  2
                                                           Col 1 Col 2 Col3
                 Here, the entries in the columns represent the number of oranges and apples bought by Ganga, Hemant and Gargi
                 respectively.

                 We denote matrices by capital letters. For example:
                                                                     2  7 
                                                                        
                                                               A =   0  5 
                                                                     −  
                                                                     3  1     


                        Order of Matrix



                 A matrix having m rows and n columns is called a matrix of order m × n or simply m × n
                 matrix (read as an m by n matrix). So, referring to the above example, matrix A is a 3 × 2 matrix. The number of
                 elements present in a matrix is given by m x n => 3 x 2 = 6 elements.
                 Each individual element is represented as a  where i represents row and j represents column.
                                                       ij
                                                                2   4    3  
                                                            A =   a11  a12  a13 
                                                                7   5    9 a23    
                                                                 a21  a22
                                                                                                    th
                                                               th
                 In general, a , is an element lying in the i  row and j  column. We can also call it as the (i, j)  element of the matrix.
                                                     th
                            ij
                        Types of Matrices

                 Matrices can be of many types:

                    • Row Matrix: Matrices having only one row are known as row matrix.
                                                    A =      2 45  13
                                                                 × 
                    • Column Matrix: Matrices having only one column are known as column matrix.
                                                          3 
                                                        
                                                    A = − 1   
                                                        
                                                          2  
                                                            31
                                                            ×
                    • Square Matrix: Matrices having equal number of rows and columns are known as square matrix.
                                                       3  4    --5 3     =
                                                             
                                                       
                                                    A = 1  A = − 2    1  Since m n
                                                           7 
                                                               
                                                       
                                                                    Order⇒×
                                                                           m m
                                                        8--3     11    2 
                                                               33×
                                                                 x
                                                                 33
                    • Diagonal Matrix: A matrix with all the elements zero except its leading diagonal is known as a diagonal
                   matrix.
                                                      20 0  
                                                      
                                                   A = 070      Also called Primary Diagonal
                                                      
                                                       006  
                                                            
                    • Scalar Matrix: A matrix in which all the diagonal elements are equal and all other elements are zero is
                   known as a scalar matrix.
                                                                                                 Maths for AI   161
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