Solution of this linear algebra system?

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I'm reading about Gauss elimination and I'm stuck on this problem:



enter image description here



So I started by adding -1 * first row to the second row and third row to produce:



$$a_0 + a_1 + a_2 = 4$$
$$a_1 + 3a_2 = -4$$
$$2a_1 + 8a_2 = 8$$



Is that right? From here where do I go?



EDIT
Is this right? Then add the multiple of -2 of the second row to the third row to get:



$$a_0 + a_1 + a_2 = 4$$
$$a_1 + 3a_2 = -4$$
$$2a_2 = 16$$



So:



$$a_0 = 24$$
$$a_1 = -28$$
$$a_2 = 8$$



Does that look right?




linear-algebra




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  • It's OK, continue eliminating $a_1$ from the third row, etc., etc.
    – Parcly Taxel
    Jul 16 at 15:59














up vote
1
down vote

favorite












I'm reading about Gauss elimination and I'm stuck on this problem:



enter image description here



So I started by adding -1 * first row to the second row and third row to produce:



$$a_0 + a_1 + a_2 = 4$$
$$a_1 + 3a_2 = -4$$
$$2a_1 + 8a_2 = 8$$



Is that right? From here where do I go?



EDIT
Is this right? Then add the multiple of -2 of the second row to the third row to get:



$$a_0 + a_1 + a_2 = 4$$
$$a_1 + 3a_2 = -4$$
$$2a_2 = 16$$



So:



$$a_0 = 24$$
$$a_1 = -28$$
$$a_2 = 8$$



Does that look right?




linear-algebra




share|cite|improve this question





















  • It's OK, continue eliminating $a_1$ from the third row, etc., etc.
    – Parcly Taxel
    Jul 16 at 15:59












up vote
1
down vote

favorite









up vote
1
down vote

favorite











I'm reading about Gauss elimination and I'm stuck on this problem:



enter image description here



So I started by adding -1 * first row to the second row and third row to produce:



$$a_0 + a_1 + a_2 = 4$$
$$a_1 + 3a_2 = -4$$
$$2a_1 + 8a_2 = 8$$



Is that right? From here where do I go?



EDIT
Is this right? Then add the multiple of -2 of the second row to the third row to get:



$$a_0 + a_1 + a_2 = 4$$
$$a_1 + 3a_2 = -4$$
$$2a_2 = 16$$



So:



$$a_0 = 24$$
$$a_1 = -28$$
$$a_2 = 8$$



Does that look right?




linear-algebra




share|cite|improve this question













I'm reading about Gauss elimination and I'm stuck on this problem:



enter image description here



So I started by adding -1 * first row to the second row and third row to produce:



$$a_0 + a_1 + a_2 = 4$$
$$a_1 + 3a_2 = -4$$
$$2a_1 + 8a_2 = 8$$



Is that right? From here where do I go?



EDIT
Is this right? Then add the multiple of -2 of the second row to the third row to get:



$$a_0 + a_1 + a_2 = 4$$
$$a_1 + 3a_2 = -4$$
$$2a_2 = 16$$



So:



$$a_0 = 24$$
$$a_1 = -28$$
$$a_2 = 8$$



Does that look right?





linear-algebra





share|cite|improve this question












share|cite|improve this question




share|cite|improve this question








edited Jul 16 at 16:12
























asked Jul 16 at 15:57









Jwan622

1,61211224




1,61211224











  • It's OK, continue eliminating $a_1$ from the third row, etc., etc.
    – Parcly Taxel
    Jul 16 at 15:59
















  • It's OK, continue eliminating $a_1$ from the third row, etc., etc.
    – Parcly Taxel
    Jul 16 at 15:59















It's OK, continue eliminating $a_1$ from the third row, etc., etc.
– Parcly Taxel
Jul 16 at 15:59




It's OK, continue eliminating $a_1$ from the third row, etc., etc.
– Parcly Taxel
Jul 16 at 15:59










1 Answer
1






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up vote
1
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In augmented matrix form we have



$$left[beginarrayc
1& 1& 1& 4\
1& 2& 4& 0\
1& 3& 9& 12
endarrayright] to left[beginarrayc
1& 1& 1& 4\
0& 1& 3& -4\
0& 2& 8& 8
endarrayright] to left[beginarrayc
1& 1& 1& 4\
0& 1& 3& -4\
0& 0& 2& 16
endarrayright]$$



that is



  • $a_2=8$

  • $a_1=-28$

  • $a_0=24$





share|cite|improve this answer





















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    1 Answer
    1






    active

    oldest

    votes








    1 Answer
    1






    active

    oldest

    votes









    active

    oldest

    votes






    active

    oldest

    votes








    up vote
    1
    down vote



    accepted










    In augmented matrix form we have



    $$left[beginarrayc
    1& 1& 1& 4\
    1& 2& 4& 0\
    1& 3& 9& 12
    endarrayright] to left[beginarrayc
    1& 1& 1& 4\
    0& 1& 3& -4\
    0& 2& 8& 8
    endarrayright] to left[beginarrayc
    1& 1& 1& 4\
    0& 1& 3& -4\
    0& 0& 2& 16
    endarrayright]$$



    that is



    • $a_2=8$

    • $a_1=-28$

    • $a_0=24$





    share|cite|improve this answer

























      up vote
      1
      down vote



      accepted










      In augmented matrix form we have



      $$left[beginarrayc
      1& 1& 1& 4\
      1& 2& 4& 0\
      1& 3& 9& 12
      endarrayright] to left[beginarrayc
      1& 1& 1& 4\
      0& 1& 3& -4\
      0& 2& 8& 8
      endarrayright] to left[beginarrayc
      1& 1& 1& 4\
      0& 1& 3& -4\
      0& 0& 2& 16
      endarrayright]$$



      that is



      • $a_2=8$

      • $a_1=-28$

      • $a_0=24$





      share|cite|improve this answer























        up vote
        1
        down vote



        accepted







        up vote
        1
        down vote



        accepted






        In augmented matrix form we have



        $$left[beginarrayc
        1& 1& 1& 4\
        1& 2& 4& 0\
        1& 3& 9& 12
        endarrayright] to left[beginarrayc
        1& 1& 1& 4\
        0& 1& 3& -4\
        0& 2& 8& 8
        endarrayright] to left[beginarrayc
        1& 1& 1& 4\
        0& 1& 3& -4\
        0& 0& 2& 16
        endarrayright]$$



        that is



        • $a_2=8$

        • $a_1=-28$

        • $a_0=24$





        share|cite|improve this answer













        In augmented matrix form we have



        $$left[beginarrayc
        1& 1& 1& 4\
        1& 2& 4& 0\
        1& 3& 9& 12
        endarrayright] to left[beginarrayc
        1& 1& 1& 4\
        0& 1& 3& -4\
        0& 2& 8& 8
        endarrayright] to left[beginarrayc
        1& 1& 1& 4\
        0& 1& 3& -4\
        0& 0& 2& 16
        endarrayright]$$



        that is



        • $a_2=8$

        • $a_1=-28$

        • $a_0=24$






        share|cite|improve this answer













        share|cite|improve this answer



        share|cite|improve this answer











        answered Jul 16 at 16:00









        gimusi

        65.4k73684




        65.4k73684






















             

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