Solution of this linear algebra system?

Clash Royale CLAN TAG#URR8PPP

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

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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edited Jul 16 at 16:12

asked Jul 16 at 15:57

Jwan622

1,61211224

• 
  
  
  

  
  

  
  
  
  
  
  

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

  
  
  
  

add a comment | 

up vote
1
down vote

favorite

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

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

edited Jul 16 at 16:12

asked Jul 16 at 15:57

Jwan622

1,61211224

• 
  
  
  

  
  

  
  
  
  
  
  

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

  
  
  
  

add a comment | 

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:

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

edited Jul 16 at 16:12

asked Jul 16 at 15:57

Jwan622

1,61211224

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

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

edited Jul 16 at 16:12

asked Jul 16 at 15:57

Jwan622

1,61211224

share|cite|improve this question

share|cite|improve this question

edited Jul 16 at 16:12

edited Jul 16 at 16:12

edited Jul 16 at 16:12

asked Jul 16 at 15:57

Jwan622

1,61211224

asked Jul 16 at 15:57

Jwan622

1,61211224

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
  

  
  
  
  

add a comment | 

• 
  
  
  

  
  

  
  
  
  
  
  

  
  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

add a comment | 

1 Answer
1

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

answered Jul 16 at 16:00

gimusi

65.4k73684

add a comment | 

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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

answered Jul 16 at 16:00

gimusi

65.4k73684

add a comment | 

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

answered Jul 16 at 16:00

gimusi

65.4k73684

add a comment | 

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

answered Jul 16 at 16:00

gimusi

65.4k73684

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

answered Jul 16 at 16:00

gimusi

65.4k73684

share|cite|improve this answer

share|cite|improve this answer

answered Jul 16 at 16:00

gimusi

65.4k73684

answered Jul 16 at 16:00

gimusi

65.4k73684

answered Jul 16 at 16:00

gimusi

65.4k73684

65.4k73684

add a comment | 

add a comment | 

 

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