Row space of a matrix - question.

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.
 

Thread 'Finding the nth roots of a complex number'

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