How to find $a_3$ and $a_4$ if $a_1$ and $a_2$ are given in a $4$×$4$ matrix [closed]

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Let $a_1, a_2, a_3, a_4$ be the four columns of a $4$×$4$ matrix $A$. If its reduced row echelon form is given by:$$left(beginmatrix 1 & 0 & 2 & 1 \ 0 & 1 & 1 & 4 \ 0 & 0 & 0 & 0 \ 0 & 0 & 0 & 0 endmatrixright)$$
and it is known that:$$a_1=beginbmatrix -3 \ 5 \ 2 \ 1 endbmatrix,a_2=beginbmatrix 4 \ -3 \ 7 \ -1 endbmatrix$$
then find $a_3$ and $a_4$.

Can anyone give hints to solve this problem.

linear-algebra

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asked Jul 15 at 3:57

philip

1289

closed as off-topic by Parcly Taxel, John Ma, hardmath, Trần Thúc Minh Trí, user223391 Jul 15 at 21:29

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Parcly Taxel, John Ma, hardmath, Trần Thúc Minh Trí, Community

If this question can be reworded to fit the rules in the help center, please edit the question.

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  Hint: How do the nonzero rows of the rref relate to the row space of the original matrix?
  – amd
  Jul 15 at 6:47
  

  
  
  
  


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  1
  

  
  
  
  
  
  

  
  It might help you if you notice that the rows of the matrix $A$ must be linear combinations of the vectors $(1,0,2,1)$, $(0,1,1,4)$.
  – Martin Sleziak
  Jul 15 at 12:52
  

  
  
  
  

add a comment | 

up vote
1
down vote

favorite

Let $a_1, a_2, a_3, a_4$ be the four columns of a $4$×$4$ matrix $A$. If its reduced row echelon form is given by:$$left(beginmatrix 1 & 0 & 2 & 1 \ 0 & 1 & 1 & 4 \ 0 & 0 & 0 & 0 \ 0 & 0 & 0 & 0 endmatrixright)$$
and it is known that:$$a_1=beginbmatrix -3 \ 5 \ 2 \ 1 endbmatrix,a_2=beginbmatrix 4 \ -3 \ 7 \ -1 endbmatrix$$
then find $a_3$ and $a_4$.

Can anyone give hints to solve this problem.

linear-algebra

share|cite|improve this question

asked Jul 15 at 3:57

philip

1289

closed as off-topic by Parcly Taxel, John Ma, hardmath, Trần Thúc Minh Trí, user223391 Jul 15 at 21:29

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Parcly Taxel, John Ma, hardmath, Trần Thúc Minh Trí, Community

If this question can be reworded to fit the rules in the help center, please edit the question.

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  Hint: How do the nonzero rows of the rref relate to the row space of the original matrix?
  – amd
  Jul 15 at 6:47
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  It might help you if you notice that the rows of the matrix $A$ must be linear combinations of the vectors $(1,0,2,1)$, $(0,1,1,4)$.
  – Martin Sleziak
  Jul 15 at 12:52
  

  
  
  
  

add a comment | 

up vote
1
down vote

favorite

up vote
1
down vote

favorite

Let $a_1, a_2, a_3, a_4$ be the four columns of a $4$×$4$ matrix $A$. If its reduced row echelon form is given by:$$left(beginmatrix 1 & 0 & 2 & 1 \ 0 & 1 & 1 & 4 \ 0 & 0 & 0 & 0 \ 0 & 0 & 0 & 0 endmatrixright)$$
and it is known that:$$a_1=beginbmatrix -3 \ 5 \ 2 \ 1 endbmatrix,a_2=beginbmatrix 4 \ -3 \ 7 \ -1 endbmatrix$$
then find $a_3$ and $a_4$.

Can anyone give hints to solve this problem.

linear-algebra

share|cite|improve this question

asked Jul 15 at 3:57

philip

1289

Let $a_1, a_2, a_3, a_4$ be the four columns of a $4$×$4$ matrix $A$. If its reduced row echelon form is given by:$$left(beginmatrix 1 & 0 & 2 & 1 \ 0 & 1 & 1 & 4 \ 0 & 0 & 0 & 0 \ 0 & 0 & 0 & 0 endmatrixright)$$
and it is known that:$$a_1=beginbmatrix -3 \ 5 \ 2 \ 1 endbmatrix,a_2=beginbmatrix 4 \ -3 \ 7 \ -1 endbmatrix$$
then find $a_3$ and $a_4$.

Can anyone give hints to solve this problem.

linear-algebra

share|cite|improve this question

asked Jul 15 at 3:57

philip

1289

share|cite|improve this question

share|cite|improve this question

asked Jul 15 at 3:57

philip

1289

asked Jul 15 at 3:57

philip

1289

asked Jul 15 at 3:57

philip

1289

1289

closed as off-topic by Parcly Taxel, John Ma, hardmath, Trần Thúc Minh Trí, user223391 Jul 15 at 21:29

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Parcly Taxel, John Ma, hardmath, Trần Thúc Minh Trí, Community

If this question can be reworded to fit the rules in the help center, please edit the question.

closed as off-topic by Parcly Taxel, John Ma, hardmath, Trần Thúc Minh Trí, user223391 Jul 15 at 21:29

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Parcly Taxel, John Ma, hardmath, Trần Thúc Minh Trí, Community

If this question can be reworded to fit the rules in the help center, please edit the question.

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  Hint: How do the nonzero rows of the rref relate to the row space of the original matrix?
  – amd
  Jul 15 at 6:47
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  It might help you if you notice that the rows of the matrix $A$ must be linear combinations of the vectors $(1,0,2,1)$, $(0,1,1,4)$.
  – Martin Sleziak
  Jul 15 at 12:52
  

  
  
  
  

add a comment | 

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  Hint: How do the nonzero rows of the rref relate to the row space of the original matrix?
  – amd
  Jul 15 at 6:47
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  It might help you if you notice that the rows of the matrix $A$ must be linear combinations of the vectors $(1,0,2,1)$, $(0,1,1,4)$.
  – Martin Sleziak
  Jul 15 at 12:52
  

  
  
  
  

1

1

Hint: How do the nonzero rows of the rref relate to the row space of the original matrix?
– amd
Jul 15 at 6:47

Hint: How do the nonzero rows of the rref relate to the row space of the original matrix?
– amd
Jul 15 at 6:47

1

1

It might help you if you notice that the rows of the matrix $A$ must be linear combinations of the vectors $(1,0,2,1)$, $(0,1,1,4)$.
– Martin Sleziak
Jul 15 at 12:52

It might help you if you notice that the rows of the matrix $A$ must be linear combinations of the vectors $(1,0,2,1)$, $(0,1,1,4)$.
– Martin Sleziak
Jul 15 at 12:52

add a comment | 

1 Answer
1

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up vote
2
down vote



accepted

I have suggestion for you. Suppose that
$a_3 = [u quad y quad v quad z]^T quad a_4 = [u' , y' ,v' , z']^T$. By using the Gassian Elemination, we obtain the reduced row of the matrix A. From this we can find columns $a_3$,and $ a_4$.

share|cite|improve this answer

edited Jul 15 at 5:46

answered Jul 15 at 5:10

MichaelCarrick

1077

add a comment | 

1 Answer
1

active

oldest

votes

1 Answer
1

active

oldest

votes

active

oldest

votes

active

oldest

votes

up vote
2
down vote



accepted

I have suggestion for you. Suppose that
$a_3 = [u quad y quad v quad z]^T quad a_4 = [u' , y' ,v' , z']^T$. By using the Gassian Elemination, we obtain the reduced row of the matrix A. From this we can find columns $a_3$,and $ a_4$.

share|cite|improve this answer

edited Jul 15 at 5:46

answered Jul 15 at 5:10

MichaelCarrick

1077

add a comment | 

up vote
2
down vote



accepted

I have suggestion for you. Suppose that
$a_3 = [u quad y quad v quad z]^T quad a_4 = [u' , y' ,v' , z']^T$. By using the Gassian Elemination, we obtain the reduced row of the matrix A. From this we can find columns $a_3$,and $ a_4$.

share|cite|improve this answer

edited Jul 15 at 5:46

answered Jul 15 at 5:10

MichaelCarrick

1077

add a comment | 

up vote
2
down vote



accepted

up vote
2
down vote



accepted

I have suggestion for you. Suppose that
$a_3 = [u quad y quad v quad z]^T quad a_4 = [u' , y' ,v' , z']^T$. By using the Gassian Elemination, we obtain the reduced row of the matrix A. From this we can find columns $a_3$,and $ a_4$.

share|cite|improve this answer

edited Jul 15 at 5:46

answered Jul 15 at 5:10

MichaelCarrick

1077

I have suggestion for you. Suppose that
$a_3 = [u quad y quad v quad z]^T quad a_4 = [u' , y' ,v' , z']^T$. By using the Gassian Elemination, we obtain the reduced row of the matrix A. From this we can find columns $a_3$,and $ a_4$.

share|cite|improve this answer

edited Jul 15 at 5:46

answered Jul 15 at 5:10

MichaelCarrick

1077

share|cite|improve this answer

share|cite|improve this answer

edited Jul 15 at 5:46

edited Jul 15 at 5:46

edited Jul 15 at 5:46

answered Jul 15 at 5:10

MichaelCarrick

1077

answered Jul 15 at 5:10

MichaelCarrick

1077

answered Jul 15 at 5:10

MichaelCarrick

1077

1077

add a comment | 

add a comment |