solve the following linear system x 1 − 3 x 2 + x 3 = 1 2 x 1 − x 2 − 2 x 3 = 2 x 1 + 2 x 2 − 3 x 3 = − 1by using gauss-jordan elimination method. The augmented matrix of the linear system is ( 1 − 3 1 1 2 − 1 − 2 2 1 2 − 3 − 1 ) .By a series of elementary row operations, we have ( 1 − 3 1 1 0 5 − 4 0 0 0 0 − 2 ) .My question is, although the question asked us to solve the linear system using gauss-jordan elimination method, can we stop immediately and conclude that the linear system is inconsistent without further apply any elementary row operation to the matrix ( 1 − 3 1 1 0 5 − 4 0 0 0 0 − 2 ) until the matrix ( 1 − 3 1 1 0 5 − 4 0 0 0 0 − 2 ) is transformed into reduced-row echelon form?

Question

solve the following linear system      x    1    −  3      x    2    +      x    3    =  1  2      x    1    −      x    2    −  2      x    3    =  2      x    1    +  2      x    2    −  3      x    3    =  −  1by using gauss-jordan elimination method. The augmented matrix of the linear system is      (                            1                          −          3                          1                          1                                      2                          −          1                          −          2                          2                                      1                          2                          −          3                          −          1                      )    .By a series of elementary row operations, we have      (                            1                          −          3                          1                          1                                      0                          5                          −          4                          0                                      0                          0                          0                          −          2                      )    .My question is, although the question asked us to solve the linear system using gauss-jordan elimination method, can we stop immediately and conclude that the linear system is inconsistent without further apply any elementary row operation to the matrix      (                            1                          −          3                          1                          1                                      0                          5                          −          4                          0                                      0                          0                          0                          −          2                      )  until the matrix      (                            1                          −          3                          1                          1                                      0                          5                          −          4                          0                                      0                          0                          0                          −          2                      )  is transformed into reduced-row echelon form?

Misael Li · Accepted Answer

Yes, you can stop there and conclude that the system is inconsistent as   0  ≠  −  2. If you were to continue to reduce the matrix to reduced-row echelon form, row   3&#039;s inconsistency would remain unaffected.      (                            1                          0                          −                      7            5                                    0                                      0                          1                          −                      4            5                                    0                                      0                          0                          0                          1                      )        R    3    →  −      1    2        R    3    was performed to get the new row   3 and notice that the completely reduced-row echelon form above also has   0      x    1    +  0      x    2    +  0      x    3    =  1    ⟹    0  =  1 which is not possible, and hence the system still maintains its inconsistency.

Semaj Christian · Accepted Answer

You can conclude that the system is inconsistent, because the last row of your matrix implies that   0      x    1    +  0      x    2    +  0      x    3    =  −  2, which cannot be satisfied.

solve the following linear system x 1 </msub> − 3 x 2

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