# Row Space

#### matqkks

##### Member
Why is row space of a matrix important?

#### Sudharaka

##### Well-known member
MHB Math Helper
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
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
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.