How to solve this particular system of linear equations? [ 1 0 0 − 1 2 0 1 0 2 − 3 0 0 1 − 1 2 ]

Question

How to solve this particular system of linear equations?      [                            1                          0                          0                          −          1                          2                                      0                          1                          0                          2                          −          3                                      0                          0                          1                          −          1                          2                      ]

Carmelo Payne · Accepted Answer

From      [                            1                          0                          0                          −          1                          2                                      0                          1                          0                          2                          −          3                                      0                          0                          1                          −          1                          2                      ]  you only have to paint, no to calculate, to get the solution: expand the matrix in this      [                            1                          0                          0                          −          1                          2                                      0                          1                          0                          2                          −          3                                      0                          0                          1                          −          1                          2                                      0                          0                          0                          −          1                          0                                      0                          0                          0                          0                          −          1                      ]  way and convince yourself that the solution set is      {          [                                    2                                                −            3                                                2                                                0                                                −            1                              ]        +    t          [                                    −            1                                                2                                                −            1                                                −            1                                                0                              ]        ∣    t    ∈    R    }    .

Manteo2h · Accepted Answer

You found      {                                        x            1                    −                      x            4                                    =          2                                                  x            2                    +          2                      x            4                                    =          −          3                                                  x            3                    −                      x            4                                    =          2                        which is equivalent to      {                                        x            1                                    =                      x            3                                                            x            1                                    =          2          +                      x            4                                                            x            2                                    =          −          3          −          2                      x            4                                  So the set of solutions is  {  (  2  +      x    4    ,  −  3  −  2      x    4    ,  2  +      x    4    ,      x    4    )  :      x    4    ∈  F  }  .

How to solve this particular system of linear equations? [ <mtable rowspacing="4pt"

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