Row space of a matrix - question.

[peripatein]

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

 

[Dick]

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.

 

[peripatein]

Why are the m vectors in R^n?

 

[Dick]

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.