Page 305 - AI Ver 3.0 Class 11
P. 305

The above information can be arranged in the given tabular form:
                                             Oranges                      Apples
                 Ganga                       12                           5
                 Hemant                      10                           7
                 Gargi                         5                          2

                 And this can be represented as:
                                                                   é
                                                              Row 1 12   5 ù  ú
                                                                   ê
                                                                   ê
                                                              Row 2 10   7 ú
                                                                   ê      ú
                                                                   ê
                                                              Row 3 5    2ú
                                                                   ë      û
                                                                 Col1 Col2
                 The entries in the rows represent number of oranges and apples bought by Ganga, Hemant, and Gargi respectively. It
                 can also be represented in another form as:
                                                          é  12  10    5 –Row1
                                                                        ù
                                                          ê             ú
                                                          ê  5   7     2 –Row 2
                                                                        ú
                                                          ë             û
                                                          Col1 Col2 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:
                                                                   é    7  ù
                                                                   ê  2  ú
                                                                   ê
                                                                A= 0    5 ú  ú
                                                                   ê
                                                                   ê     ú
                                                                   ê  ë  -3  1  ú  û

                        Order of Matrix


                 A matrix having m rows and n columns is called a matrix of the 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 × n ⇒ 3 × 2 = 6 elements.
                 Each individual element is represented as a  where i represents row and j represents column.
                                                       ij
                                                                2   4    3 
                                                            A =    a 11  a 12  a 13    
                                                                  7   a 21  5 a 22  9 a 23 
                                                                                                   th
                                                     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.
                            ij
                                 Task                                              #Problem Solving & Logical Reasoning


                     Given the following matrix, identify the following elements:

                              76  − 5
                         A =     40  2   
                              3 8  10  −
                                     
                     a.  a                             b.  a                        c.   a 31
                         23
                                                            11




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