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Step 6:   Covering the second row and third column.
                                                       2 − 1 0
                                                                2 − 1
                                                                         2
                                                              
                                                       1  0 2 ⇒  1  1  ⇒− −(  1 ⇒)  3
                                                       1   1 3  
                 Step 7:   Covering the third row and first column.
                                                       2   − 10
                                                                − 10
                                                                            −
                                                              
                                                        1  0 2 ⇒  02   ⇒− 20 ⇒ −  2
                                                        1   13   
                 Step 8:   Covering the third row and second column.
                                                         2 − 1 0
                                                                  20
                                                                          40
                                                                
                                                         1  0 2 ⇒  12  ⇒ −⇒     4
                                                         1   1 3  
                 Step 9:   Covering the third row and third column.
                                                       2   − 10
                                                                 2  − 1
                                                                          0 ( 1) ⇒
                                                               
                                                        1  0 2 ⇒  1   0  ⇒ − −    1
                                                        1   13   
                 Writing all values in matrix representation.

                                                (
                                               + − )  − 1  +  1  −  2  −1  1 
                                                 2
                                                                         
                                                (
                                                 3
                                               − − )  + 6  −3   ⇒    3  6  −3 
                                               + − )  − 4  +  1   −2  −4  1 
                                                (
                                                 2
                                                                           Co factor Matrix
                 (In this step, we add the positive (+) and the negative (–) signs before each element alternatively.)
                 Adj (A) = Transpose of the co factor matrix.
                                                                                              2      2 
                                                                                                 − 1   
                                           −  2  −  1  1    −  2  3  2−    2  3  −  2−    3    3  
                                 Adj(A) =      3  6 −  3 =          −  1  6 −  4     A − 1  =  1     −  1  6  −  4 ⇒          1  −  2  4   
                                           −  2 −  1     1 −  1      − 3   1  3   1    −  3    3  
                                             4           3                              −  1   −  1 
                                                                                                3  1  3   
                                   −
                               So,A =  1  Adj(A)
                                   1
                                           A                                                 Final Answer
                        Vector Arithmetic


                 Vectors are the basis of linear algebra. Vectors are used in the training of machine learning algorithms. When describing
                 the machine learning algorithm, the target variable is usually expressed as a vector with a lowercase “y”.

                 A vector is defined as a list of numbers in one-dimensional form. For example:
                                                             2 2
                                                               
                                                                         −
                                                                          3 6
                                                                      1
                                                                               
                                                             −− 55     1 − 3 6
                                                                     
                                                              4  4 
                                                               
                                                            
                                                    (one column)      (one row)
                 A vector is an object that has both a magnitude and a direction. It is represented as ai + bj + ck where i, j, k are the
                 directions along the x, y, and z axes respectively.


                                                                                                 Maths for AI   169
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