I'm having a hard time understanding this question:Determine the reduced echelon form of the homogeneous linear system of three equations in variables x 1 , x 2 , x 3 , x 4 , x 5 such that x 1 , x 2 , x 4 are leading variables; x 3 , x 5 are free variables and which has solutions ( 2 − 1 1 0 0 ) and ( − 3 2 0 − 4 1 )

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I&#039;m having a hard time understanding this question:Determine the reduced echelon form of the homogeneous linear system of three equations in variables       x          1        ,      x          2        ,      x          3        ,      x          4        ,      x          5       such that       x          1        ,      x          2        ,      x          4       are leading variables;       x          3        ,      x          5       are free variables and which has solutions      (                            2                                      −          1                                      1                                      0                                      0                      )      and        (                            −          3                                      2                                      0                                      −          4                                      1                      )

Jaelynn Cuevas · Accepted Answer

You have      {                                        x            1                    =          2                      x            3                    −          3                      x            5                                                            x            2                    =          −                      x            3                    +          2                      x            5                                                            x            4                    =          −          4                      x            5                                  which means      {                                        x            1                    −          2                      x            3                    +          3                      x            5                    =          0                                                  x            2                    +                      x            3                    −          2                      x            5                    =          0                                                  x            4                    +          4                      x            5                    =          0                        This system&#039;s matrix is what you&#039;re looking for.If you can&#039;t see why, here&#039;s a different strategy: the matrix must be of the form      [                            1                          0                          a                          0                          b                                      0                          1                          c                          0                          d                                      0                          0                          0                          1                          e                      ]  and the two given vectors should be in its null space.

I'm having a hard time understanding this question: Determine the reduced echelon form of the homog

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