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Row Space

matqkks

Member
Jun 26, 2012
74
Why is row space of a matrix important?
 

Sudharaka

Well-known member
MHB Math Helper
Feb 5, 2012
1,621
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.
 

matqkks

Member
Jun 26, 2012
74
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?'
 

Sudharaka

Well-known member
MHB Math Helper
Feb 5, 2012
1,621
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 this).

Kind Regards,
Sudharaka.