Page 167 - Artificial Intellegence_v2.0_Class_11
P. 167

Take the second row of matrix A and first column of matrix B. Multiple the corresponding elements and then add them
                 as shown. Repeat this step for all columns of B.
                 Step 4:        51    26 0  
                             A =      B=    
                                 23    13 4 
                                            11 33 4
                                ×
                        ⇒ 2 2 31 ⇒   7 ⇒          
                             +
                           ×
                                            7  ?  ? 
                 Step 5:     51       26 0  
                          A =      B =      
                              23       13 4 
                                           11 33 4
                           ×
                        ⇒ 2 6 3 3 ⇒  21⇒         
                                ×
                             +
                                           7  21 ?  
                 Step 6:       51       26 0   
                            A  =      B =      
                                23       13 4  
                                             11 33 4 
                             +
                                ×
                        ⇒ 2 034⇒     12 ⇒           
                           ×
                                             7  21 12 
                            Finally   AB =      11 33  4   
                                            7  21 12   23
                                                      ×
                                 Reboot


                       1.  If a matrix has 6 elements, what are the possible orders it can have?
                         ___________________________________________________________________________
                         ___________________________________________________________________________

                                                                                 2i
                       2.  Construct a 3 x 2 matrix where each element is given by a =  .
                                                                              ij
                                                                                 j
                         ___________________________________________________________________________
                         ___________________________________________________________________________




                 Determinants
                 In mathematics, the determinant is a scalar value that is a function of the entries of a square matrix. This function
                 can be a real number or a complex number, but it is unique. The determinant of a matrix A is denoted by det(A), det
                 A, or |A|.

                    1.  Determinant of 1x1 matrix: The determinant of a matrix A= [a ] is the element a . For example:
                                                                              ij
                                                                                              ij
                                                              A   11  A3
                                                                =
                                                                         =
                                                                  3
                                                                 
                                                                     ×
                    2.  Determinant of 2 x 2 matrix: If A is a 2 x 2 matrix then the determinant of A is defined as a a – a a .
                                                                                                               21 12
                                                                                                       11 22
                                                   a   a 
                                                                          −
                                               A =   11  12   A = ( a × a ) ( a × a )
                                                                                  12
                                                                              21
                                                                    11
                                                   a
                                                                        22
                                                   21  a 22 
                                                     1     3
                                                                       −− × )
                                                 A =        A = 1(  × 4 ) (  23 =10
                                                     −2  4 
                                                                                                 Maths for AI   165
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