MHB The Significance of Row Space in a Matrix

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The row space of a matrix is significant as it helps define the rank of the matrix, which is crucial for understanding the solutions to linear systems. While the column space directly relates to the existence of solutions in the equation Ax=b, the row space provides insights into the matrix's properties and dimensionality. Understanding row space can enhance students' grasp of linear algebra concepts and their applications. It is particularly relevant in contexts where determining the rank is necessary for solving problems. Overall, learning about row space enriches the foundational knowledge of matrix theory.
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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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