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Linear Algebra isomorphism exercise1

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-1

$begingroup$

enter image description here

In this question, why don't I need to verify that $V longrightarrow R^2$ is one-one?
Linear transformation does not ensure that it is one to one.

linear-transformations

share|cite|improve this question

edited Mar 16 at 9:49

Bernard

123k741117

asked Mar 16 at 9:08

주혜민주혜민

1

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Please do not use pictures (even not correctly rotated).
  $endgroup$
  – Dietrich Burde
  Mar 16 at 9:10
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  You're asked to describe an isomorphism. By definition an isomorphism is, not only linear, but also one-one and onto.
  $endgroup$
  – Bernard
  Mar 16 at 9:54
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Why shouldn't I use pictures? I'm sorry about the rotated picture, but I haven't looked the rule that we should not upload pictures. If you don't mind, can you show me the rule related to the picture?
  $endgroup$
  – 주혜민
  Mar 16 at 11:15
  

  
  
  
  

add a comment | 

-1

$begingroup$

enter image description here

In this question, why don't I need to verify that $V longrightarrow R^2$ is one-one?
Linear transformation does not ensure that it is one to one.

linear-transformations

share|cite|improve this question

edited Mar 16 at 9:49

Bernard

123k741117

asked Mar 16 at 9:08

주혜민주혜민

1

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Please do not use pictures (even not correctly rotated).
  $endgroup$
  – Dietrich Burde
  Mar 16 at 9:10
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  You're asked to describe an isomorphism. By definition an isomorphism is, not only linear, but also one-one and onto.
  $endgroup$
  – Bernard
  Mar 16 at 9:54
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Why shouldn't I use pictures? I'm sorry about the rotated picture, but I haven't looked the rule that we should not upload pictures. If you don't mind, can you show me the rule related to the picture?
  $endgroup$
  – 주혜민
  Mar 16 at 11:15
  

  
  
  
  

add a comment | 

$begingroup$

enter image description here

In this question, why don't I need to verify that $V longrightarrow R^2$ is one-one?
Linear transformation does not ensure that it is one to one.

linear-transformations

share|cite|improve this question

edited Mar 16 at 9:49

Bernard

123k741117

asked Mar 16 at 9:08

주혜민주혜민

1

$endgroup$

share|cite|improve this question

edited Mar 16 at 9:49

Bernard

123k741117

asked Mar 16 at 9:08

주혜민주혜민

1

share|cite|improve this question

edited Mar 16 at 9:49

Bernard

123k741117

asked Mar 16 at 9:08

주혜민주혜민

1

edited Mar 16 at 9:49

Bernard

123k741117

edited Mar 16 at 9:49

Bernard

123k741117

asked Mar 16 at 9:08

주혜민주혜민

1

asked Mar 16 at 9:08

주혜민주혜민

1