Write the following system of equations in the form A X = B, and calculate the solution using the equation 2 x − 3 y = − 1. 2 x − 3 y = − 1 − 5 x + 5 y = 20

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Write the following system of equations in the form   A  X  =  B, and calculate the solution using the equation   2  x  −  3  y  =  −  1.  2  x  −  3  y  =  −  1  −  5  x  +  5  y  =  20

HTMW7C0a · Accepted Answer

Let   X  =      [                            x                                      y                      ]  , then the first equation can be written, in matrix multiplication, as      [                            2                          −          3                      ]        [                            x                                      y                      ]    =      [                            −          1                      ]  Similarly, the second equation can be written as      [                            −          5                          5                      ]        [                            x                                      y                      ]    =      [                            20                      ]  By combining these two equations as a system, they can be written as                              [                                                    2                                            −                3                                                                    −                5                                            5                                              ]                          [                                                    x                                                                    y                                              ]                                    =                  [                                                    −                1                                                                    20                                              ]                                    A        X                            =        B            Now, if the above   A has an inverse, then both sides can be left-multiplied by       A          −      1       to get                    A        X                            =        B                                      A                      −            1                          A        X                            =                  A                      −            1                          B                                      I          2                X                            =                  A                      −            1                          B                            X                            =                  A                      −            1                          B                                      [                                                    x                                                                    y                                              ]                                    =                              [                                                            2                                                  −                  3                                                                              −                  5                                                  5                                                      ]                                −            1                                    [                                                    −                1                                                                    20                                              ]                    And then the original unknowns in the system of equation can be solved.

Write the following system of equations in the form A X = B , and calculate the soluti

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