MHB The Significance of Row Space in a Matrix

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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