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−
                                                                                −
                                                      =  1 (0 40) −  2(0 35) +  3(32 0)
                                                           −
                                                            +
                                                      =  −  40 70 96
                                                                +
                                                         =
                                                       A 126
                                 Task



                     Calculate the determinant of the following matrices:
                             13 2
                     1.  A =     60 0   
                             75 4 
                                  

                             2 4
                     2.  A =   
                             38 




                 Inverse of a Matrix
                 For matrices, division is undefined. There is a related concept, called “inversion”. Matrix inversion is a process of
                 finding another matrix that when multiplied with the original matrix, gives an identity matrix.
                               1        1
                 6                   6×   =  1
                   Reciprocal  6        6

                                         –1
                 A             A –1  A × A = I (Identity Matrix)
                     Inverse
                 Calculating Inverse of a Matrix
                 Following are the steps in order to calculate the inverse of a matrix:
                    • Inverse of 2x2 Matrix: Consider matrix A given by:

                                                                      ab
                                                                 A =    
                                                                      cd 
                                                             -1
                    Then the inverse of the matrix A, denoted by A  is given by:
                                                         1   d  − b  This matrix is also
                                                      −
                                                    A =             called adjoint.
                                                      1
                                                         A − c  a  
                                                           
                                                    determinant
                   Rules:
                    1.   To calculate the adjoint of a matrix – In matrix A, SWAP (interchange) the positions of elements a and d. Also,
                      put a negative (minus) sign in front of elements b and c.
                    2.  Divide all elements by the determinant.
                    For example:
                                                                              65
                                                       Find the inverse of A  =   
                                                                              21 
                                                             65
                                                                    ×− ×= − 4
                                                         A =     = 61 25
                                                             21
                                                                                                 Maths for AI   167
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