If we have an $n times m$ matrix $A$, is Col(A) a subspace of $mathbbR^m$? [closed]

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I am reading through Axler's Linear Algebra book.

I believe that the answer to my question is no.

This link shows that if we have an $n times m$ matrix $A$, then Col(A) is a subspace of $mathbbR^n$, but I cannot come up with a similar proof to show that the same holds for $mathbbR^m$. For example, consder $m > n$.

Thanks.

linear-algebra

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asked Jul 23 at 21:32

Hat

789115

closed as off-topic by John Ma, Xander Henderson, Claude Leibovici, Taroccoesbrocco, Mostafa Ayaz Jul 29 at 19:54

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." – Xander Henderson, Claude Leibovici, Taroccoesbrocco, Mostafa Ayaz

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

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up vote
0
down vote

favorite

1

I am reading through Axler's Linear Algebra book.

I believe that the answer to my question is no.

This link shows that if we have an $n times m$ matrix $A$, then Col(A) is a subspace of $mathbbR^n$, but I cannot come up with a similar proof to show that the same holds for $mathbbR^m$. For example, consder $m > n$.

Thanks.

linear-algebra

share|cite|improve this question

asked Jul 23 at 21:32

Hat

789115

closed as off-topic by John Ma, Xander Henderson, Claude Leibovici, Taroccoesbrocco, Mostafa Ayaz Jul 29 at 19:54

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." – Xander Henderson, Claude Leibovici, Taroccoesbrocco, Mostafa Ayaz

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

add a comment | 

up vote
0
down vote

favorite

1

up vote
0
down vote

favorite

1

1

I am reading through Axler's Linear Algebra book.

I believe that the answer to my question is no.

This link shows that if we have an $n times m$ matrix $A$, then Col(A) is a subspace of $mathbbR^n$, but I cannot come up with a similar proof to show that the same holds for $mathbbR^m$. For example, consder $m > n$.

Thanks.

linear-algebra

share|cite|improve this question

asked Jul 23 at 21:32

Hat

789115

I am reading through Axler's Linear Algebra book.

I believe that the answer to my question is no.

This link shows that if we have an $n times m$ matrix $A$, then Col(A) is a subspace of $mathbbR^n$, but I cannot come up with a similar proof to show that the same holds for $mathbbR^m$. For example, consder $m > n$.

Thanks.

linear-algebra

share|cite|improve this question

asked Jul 23 at 21:32

Hat

789115

share|cite|improve this question

share|cite|improve this question

asked Jul 23 at 21:32

Hat

789115

asked Jul 23 at 21:32

Hat

789115

asked Jul 23 at 21:32

Hat

789115

789115

closed as off-topic by John Ma, Xander Henderson, Claude Leibovici, Taroccoesbrocco, Mostafa Ayaz Jul 29 at 19:54

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." – Xander Henderson, Claude Leibovici, Taroccoesbrocco, Mostafa Ayaz

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

closed as off-topic by John Ma, Xander Henderson, Claude Leibovici, Taroccoesbrocco, Mostafa Ayaz Jul 29 at 19:54

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." – Xander Henderson, Claude Leibovici, Taroccoesbrocco, Mostafa Ayaz

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

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add a comment | 

1 Answer
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accepted

Note that for a n-by m matrix any vectors in Col(A) is in $mathbbR^n$ therefore Col(A) is a subspace of $mathbbR^n$ and Row(A) is a subspace of $mathbbR^m$.

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answered Jul 23 at 21:35

gimusi

65.2k73583

• 
  
  
  

  
  

  
  
  
  
  
  

  
  That's what I thought, thanks.
  – Hat
  Jul 23 at 21:35
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @Hat That was a nice thought! You are welcome, Bye.
  – gimusi
  Jul 23 at 21:36
  

  
  
  
  

add a comment | 

1 Answer
1

active

oldest

votes

1 Answer
1

active

oldest

votes

active

oldest

votes

active

oldest

votes

up vote
1
down vote



accepted

Note that for a n-by m matrix any vectors in Col(A) is in $mathbbR^n$ therefore Col(A) is a subspace of $mathbbR^n$ and Row(A) is a subspace of $mathbbR^m$.

share|cite|improve this answer

answered Jul 23 at 21:35

gimusi

65.2k73583

• 
  
  
  

  
  

  
  
  
  
  
  

  
  That's what I thought, thanks.
  – Hat
  Jul 23 at 21:35
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @Hat That was a nice thought! You are welcome, Bye.
  – gimusi
  Jul 23 at 21:36
  

  
  
  
  

add a comment | 

up vote
1
down vote



accepted

Note that for a n-by m matrix any vectors in Col(A) is in $mathbbR^n$ therefore Col(A) is a subspace of $mathbbR^n$ and Row(A) is a subspace of $mathbbR^m$.

share|cite|improve this answer

answered Jul 23 at 21:35

gimusi

65.2k73583

• 
  
  
  

  
  

  
  
  
  
  
  

  
  That's what I thought, thanks.
  – Hat
  Jul 23 at 21:35
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @Hat That was a nice thought! You are welcome, Bye.
  – gimusi
  Jul 23 at 21:36
  

  
  
  
  

add a comment | 

up vote
1
down vote



accepted

up vote
1
down vote



accepted

Note that for a n-by m matrix any vectors in Col(A) is in $mathbbR^n$ therefore Col(A) is a subspace of $mathbbR^n$ and Row(A) is a subspace of $mathbbR^m$.

share|cite|improve this answer

answered Jul 23 at 21:35

gimusi

65.2k73583

Note that for a n-by m matrix any vectors in Col(A) is in $mathbbR^n$ therefore Col(A) is a subspace of $mathbbR^n$ and Row(A) is a subspace of $mathbbR^m$.

share|cite|improve this answer

answered Jul 23 at 21:35

gimusi

65.2k73583

share|cite|improve this answer

share|cite|improve this answer

answered Jul 23 at 21:35

gimusi

65.2k73583

answered Jul 23 at 21:35

gimusi

65.2k73583

answered Jul 23 at 21:35

gimusi

65.2k73583

65.2k73583

• 
  
  
  

  
  

  
  
  
  
  
  

  
  That's what I thought, thanks.
  – Hat
  Jul 23 at 21:35
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @Hat That was a nice thought! You are welcome, Bye.
  – gimusi
  Jul 23 at 21:36
  

  
  
  
  

add a comment | 

• 
  
  
  

  
  

  
  
  
  
  
  

  
  That's what I thought, thanks.
  – Hat
  Jul 23 at 21:35
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @Hat That was a nice thought! You are welcome, Bye.
  – gimusi
  Jul 23 at 21:36
  

  
  
  
  

That's what I thought, thanks.
– Hat
Jul 23 at 21:35

That's what I thought, thanks.
– Hat
Jul 23 at 21:35

@Hat That was a nice thought! You are welcome, Bye.
– gimusi
Jul 23 at 21:36

@Hat That was a nice thought! You are welcome, Bye.
– gimusi
Jul 23 at 21:36

add a comment |