What am I doing wrong solving this system of equations?

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$$begincases
2x_1+5x_2-8x_3=8\
4x_1+3x_2-9x_3=9\
2x_1+3x_2-5x_3=7\
x_1+8x_2-7x_3=12
endcases$$



From my elementary row operations, I get that it has no solution.



solving a system of equations



However, the answer in the book $(3, 2, 1)$ fits the system.



Was there an arithmetical mistake, or do I misunderstand something fundamentally?



Thank you.






linear-algebra systems-of-equations







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  • 4




    It is in your best interest that you type your questions (using MathJax) instead of posting links to pictures.
    – José Carlos Santos
    42 mins ago






  • 2




    I would also recommend simply checking answers via a computer, you can quickly see your arithmetic mistake matrix.reshish.com/gauss-jordanElimination.php . Even the most experienced mathematicians still make minus sign errors or simple multiplication errors. We're mathematicians after all, not primary school teachers :P
    – WesleyGroupshaveFeelingsToo
    17 mins ago














up vote
3
down vote

favorite












$$begincases
2x_1+5x_2-8x_3=8\
4x_1+3x_2-9x_3=9\
2x_1+3x_2-5x_3=7\
x_1+8x_2-7x_3=12
endcases$$



From my elementary row operations, I get that it has no solution.



solving a system of equations



However, the answer in the book $(3, 2, 1)$ fits the system.



Was there an arithmetical mistake, or do I misunderstand something fundamentally?



Thank you.






linear-algebra systems-of-equations







share|cite|improve this question

















  • 4




    It is in your best interest that you type your questions (using MathJax) instead of posting links to pictures.
    – José Carlos Santos
    42 mins ago






  • 2




    I would also recommend simply checking answers via a computer, you can quickly see your arithmetic mistake matrix.reshish.com/gauss-jordanElimination.php . Even the most experienced mathematicians still make minus sign errors or simple multiplication errors. We're mathematicians after all, not primary school teachers :P
    – WesleyGroupshaveFeelingsToo
    17 mins ago












up vote
3
down vote

favorite









up vote
3
down vote

favorite











$$begincases
2x_1+5x_2-8x_3=8\
4x_1+3x_2-9x_3=9\
2x_1+3x_2-5x_3=7\
x_1+8x_2-7x_3=12
endcases$$



From my elementary row operations, I get that it has no solution.



solving a system of equations



However, the answer in the book $(3, 2, 1)$ fits the system.



Was there an arithmetical mistake, or do I misunderstand something fundamentally?



Thank you.






linear-algebra systems-of-equations







share|cite|improve this question













$$begincases
2x_1+5x_2-8x_3=8\
4x_1+3x_2-9x_3=9\
2x_1+3x_2-5x_3=7\
x_1+8x_2-7x_3=12
endcases$$



From my elementary row operations, I get that it has no solution.



solving a system of equations



However, the answer in the book $(3, 2, 1)$ fits the system.



Was there an arithmetical mistake, or do I misunderstand something fundamentally?



Thank you.






linear-algebra systems-of-equations




linear-algebra systems-of-equations






share|cite|improve this question













share|cite|improve this question











share|cite|improve this question




share|cite|improve this question










asked 43 mins ago









fragileradius

1589




1589







  • 4




    It is in your best interest that you type your questions (using MathJax) instead of posting links to pictures.
    – José Carlos Santos
    42 mins ago






  • 2




    I would also recommend simply checking answers via a computer, you can quickly see your arithmetic mistake matrix.reshish.com/gauss-jordanElimination.php . Even the most experienced mathematicians still make minus sign errors or simple multiplication errors. We're mathematicians after all, not primary school teachers :P
    – WesleyGroupshaveFeelingsToo
    17 mins ago












  • 4




    It is in your best interest that you type your questions (using MathJax) instead of posting links to pictures.
    – José Carlos Santos
    42 mins ago






  • 2




    I would also recommend simply checking answers via a computer, you can quickly see your arithmetic mistake matrix.reshish.com/gauss-jordanElimination.php . Even the most experienced mathematicians still make minus sign errors or simple multiplication errors. We're mathematicians after all, not primary school teachers :P
    – WesleyGroupshaveFeelingsToo
    17 mins ago







4




4




It is in your best interest that you type your questions (using MathJax) instead of posting links to pictures.
– José Carlos Santos
42 mins ago




It is in your best interest that you type your questions (using MathJax) instead of posting links to pictures.
– José Carlos Santos
42 mins ago




2




2




I would also recommend simply checking answers via a computer, you can quickly see your arithmetic mistake matrix.reshish.com/gauss-jordanElimination.php . Even the most experienced mathematicians still make minus sign errors or simple multiplication errors. We're mathematicians after all, not primary school teachers :P
– WesleyGroupshaveFeelingsToo
17 mins ago




I would also recommend simply checking answers via a computer, you can quickly see your arithmetic mistake matrix.reshish.com/gauss-jordanElimination.php . Even the most experienced mathematicians still make minus sign errors or simple multiplication errors. We're mathematicians after all, not primary school teachers :P
– WesleyGroupshaveFeelingsToo
17 mins ago










2 Answers
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up vote
6
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Hint: Try inputing the solution $(3,2,1)$ into every step. That will allow you to identify the step where you went wrong.






share|cite|improve this answer



























    up vote
    3
    down vote













    You do (in the third matrix): $$L3-L4=(0, -3, 1 mid -5)-(0, -13, 9 mid -19)=(0, 10, -8 mid 12)$$ but you have $(0, 10, 8 mid -12)$ instead.






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      2 Answers
      2






      active

      oldest

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      2 Answers
      2






      active

      oldest

      votes









      active

      oldest

      votes






      active

      oldest

      votes








      up vote
      6
      down vote



      accepted










      Hint: Try inputing the solution $(3,2,1)$ into every step. That will allow you to identify the step where you went wrong.






      share|cite|improve this answer
























        up vote
        6
        down vote



        accepted










        Hint: Try inputing the solution $(3,2,1)$ into every step. That will allow you to identify the step where you went wrong.






        share|cite|improve this answer






















          up vote
          6
          down vote



          accepted







          up vote
          6
          down vote



          accepted






          Hint: Try inputing the solution $(3,2,1)$ into every step. That will allow you to identify the step where you went wrong.






          share|cite|improve this answer












          Hint: Try inputing the solution $(3,2,1)$ into every step. That will allow you to identify the step where you went wrong.







          share|cite|improve this answer












          share|cite|improve this answer



          share|cite|improve this answer










          answered 34 mins ago









          5xum

          87k388157




          87k388157




















              up vote
              3
              down vote













              You do (in the third matrix): $$L3-L4=(0, -3, 1 mid -5)-(0, -13, 9 mid -19)=(0, 10, -8 mid 12)$$ but you have $(0, 10, 8 mid -12)$ instead.






              share|cite|improve this answer


























                up vote
                3
                down vote













                You do (in the third matrix): $$L3-L4=(0, -3, 1 mid -5)-(0, -13, 9 mid -19)=(0, 10, -8 mid 12)$$ but you have $(0, 10, 8 mid -12)$ instead.






                share|cite|improve this answer
























                  up vote
                  3
                  down vote










                  up vote
                  3
                  down vote









                  You do (in the third matrix): $$L3-L4=(0, -3, 1 mid -5)-(0, -13, 9 mid -19)=(0, 10, -8 mid 12)$$ but you have $(0, 10, 8 mid -12)$ instead.






                  share|cite|improve this answer














                  You do (in the third matrix): $$L3-L4=(0, -3, 1 mid -5)-(0, -13, 9 mid -19)=(0, 10, -8 mid 12)$$ but you have $(0, 10, 8 mid -12)$ instead.







                  share|cite|improve this answer














                  share|cite|improve this answer



                  share|cite|improve this answer








                  edited 18 mins ago

























                  answered 25 mins ago









                  Jimmy R.

                  32.2k42155




                  32.2k42155



























                       

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