question_answer 73)

Find the matrix X so that                        

Answer:

Let  is the required matrix                                                 On equation corresponding elements, we get                         a + 2b = ? 7                              ? (1)                         2a + 5b = ? 8                            ? (2)                         3a + 6b = ? 9                            ?. (3)                         c + 4d = 2                                 ?. (4)                         2c + 5d = 4                               ?. (5)                         3c + 6d = 6                               ?. (6)             (2) ? 2 × (1) gives                         5b ? 8b = ? 8 + 14                                                        a ? 8 = ? 7             Clearly a = 1, b = ?2 satisfy equation (3)             Also, (5) ? 2  × (4) gives             5d ? 8d = 4 ? 4              ?3d = 0  d = 0                                     c + 0 = 2             Clearly c = 2, d = 0 satisfy equation (6).