Row space of a matrix - question.

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Homework Help Overview

The discussion revolves around understanding the concept of the row space of a matrix, specifically why it is considered a subspace of R^n rather than R^m. The original poster seeks clarification on this topic.

Discussion Character

  • Conceptual clarification

Approaches and Questions Raised

  • Participants explore the relationship between the number of rows and columns in a matrix, questioning the dimensionality of the row space. Some participants provide reasoning based on the components of the vectors represented by the rows.

Discussion Status

The discussion is ongoing, with participants questioning the reasoning behind the classification of the row space. Some guidance has been offered regarding the dimensionality based on the components of the vectors, but further clarification is still being sought.

Contextual Notes

There may be assumptions regarding the definitions of vector spaces and the properties of matrices that are being examined, but these have not been explicitly stated in the discussion.

peripatein
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Hello,

Homework Statement



Could anyone please explain why the row space of a matrix mXn over R is a subspace of R^n, and not of R^m?

Homework Equations





The Attempt at a Solution

 
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Because you have m rows and n columns and the rows are your vectors. So you have m vectors each with n components. So you have m vectors in R^n.
 
Why are the m vectors in R^n?
 
peripatein said:
Why are the m vectors in R^n?

Because they have n components. (1,2,3) is in R^3 because it has 3 components. (1,2,3,4) is in R^4. Etc.
 

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