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Basic Mathematics – I




                    Notes
                                               5  0  0
                                         5I   0   5  0
                                              0   0   5


                                                             9  4 5 8 8 0    8 8 0
                                       Adding    A  2  4A  5I  8 8 0 9  4 5 8 8 0
                                                             8 8 0   8 8 0 9    4 5


                                                             0 0 0
                                                             0 0 0    0

                                                             0 0 0


                                                            A 2  4A  5I  0.

                                                       1   2  3        2 4   8
                                          Example: If  A  4  7  5 , B  0  6  3
                                                       0  18  10      5  7 11


                                                               B
                                       Verify that  2(A B )  2A  2 .
                                  Solution:

                                               1 2   2  4  3 8
                                        A B    4 0   7  6   5 3
                                               0 5   8 7  10 11


                                               1  2  11
                                                  4  13  2
                                               5  15 21


                                                   1  2  11
                                        2(A B )  2  4  13  2
                                                   5  15 21


                                                  2  4  22
                                        2(A B )   8  26  4                                                 ...(1)
                                                 10  30 42


                                              1   2  3     2  4   6
                                        2A  2 4  7   5     8 14   10
                                              0  8  10     0 16  20


                                               2 4   8     4  8  16
                                        2B  2  0  6  3     0  12  6
                                              5   7 11    10 14 22




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