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For example:
                                                                              14  
                                                        12 3                    
                                                                           ‘
                                                     A =         A OR A = 24     
                                                                    T
                                                                              
                                                         45 6  ×23           36 
                                                                                   ×32
              Multiplication of a Matrix by a Scalar
              A scalar is any number. So, if A is a matrix and k is a scalar, then kA is another matrix which is obtained by multiplying
              each element of A by the scalar k. For example:

                                                                15 3 
                                                          A =          k3
                                                                         =
                                                                2 47 

                                                           1 3 53 33 ×    3 15 9 
                                                                ×
                                                           ×
                                                   =
                                                kA 3A =                 ⇒        
                                                           ×
                                                                    ×
                                                                ×
                                                           2 3 4 3 7 3     6 12 21 
              Multiplication of Matrices
              The product of two matrices A and B is defined if the number of columns of A is equal to the number of rows of B.
              Consider A = [a ], an m × n matrix and B = [b ] is an n × p matrix. Then the product of the matrices A and B is the
                                                        jk
                             ij
                                                                                           th
                                                                                                          th
              matrix C of order m × p. To get the (i, k)th element i.e c  of the matrix C, we take the i  row of A and k  column of B,
                                                               ik
              multiply them elementwise and take the sum of all these products. For example:
                                                       5 1        26 0
                                                  A =        B =      
                                                       2 3   2 2    13 4    23
                                                           ×
                                                                           ×
                                                                 equal                
                                                                             AB =     
                                                                                        23
                                                                                        ×
                                                                        Resultant Matrix, AB is of
                                                                        the order 2 x 3
              Take the first 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 1:        51        26 0   
                          A =        B =      
                              23        13 4  

                                                    11 ? ? 
                          ⇒ (5 2 1 1) ⇒    11 ⇒          
                                 +×
                              ×
                                                    ?  ?? 
                                          Resultant Matrix, AB getting filled

              Step 2:        51         26 0  
                          A =        B  =     
                              23         13 4 

                                               11 33 ? 
                                 +×
                          ⇒  5 6 1 3 ⇒  33 ⇒          
                              ×
                                               ?  ?  ? 
              Step 3:     A = 51    B = 26 0  
                                        
                             
                              23       13 4 
                                             11 33 4
                          ⇒  5 0 14 ⇒ ⇒             
                                +×
                              ×
                                        4
                                             ?  ?  ? 


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