The Significance of Row Space in a Matrix

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Discussion Overview

The discussion centers on the significance of the row space of a matrix, exploring its importance in linear algebra, particularly in relation to the rank of a matrix and its applications. Participants question the necessity of understanding row space compared to column space.

Discussion Character

  • Conceptual clarification, Debate/contested

Main Points Raised

  • One participant questions the importance of row space, asking why students should learn about it compared to the more straightforward concept of column space.
  • Another participant suggests that row space is important for defining the rank of a matrix, which has practical applications.
  • There is a request for clarification on what is meant by "important" in the context of row space, indicating a desire for practical connections.

Areas of Agreement / Disagreement

Participants express differing views on the importance of row space, with some emphasizing its role in defining rank while others question its relevance for students.

Contextual Notes

Some assumptions about the audience's familiarity with linear algebra concepts may be present, and the discussion does not resolve the perceived importance of row space versus column space.

matqkks
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Why is row space of a matrix important?
 
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matqkks said:
Why is row space of a matrix important?

Hi matqkks, :)

Can you elaborate what do you mean by "important"? Do you want to connect this concept with some practical applications?

Kind Regards,
Sudharaka.
 
We know that the linear system Ax=b has a solution iff b is in the column space of matrix A. So column space needs no other motivation for students. THe only time I tend to use row space is to define rank of matrix.
Really what I am asking is 'why should students want to learn about row space?'
 
matqkks said:
We know that the linear system Ax=b has a solution iff b is in the column space of matrix A. So column space needs no other motivation for students. THe only time I tend to use row space is to define rank of matrix.
Really what I am asking is 'why should students want to learn about row space?'

Well in that sense, the row space is important in establishing the rank of a matrix, which in turn has useful applications(See this and http://www.mathhelpboards.com/f14/rank-1618/#post7582).

Kind Regards,
Sudharaka.
 

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