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Row space of a matrix - question.

  1. Dec 3, 2012 #1
    Hello,

    1. The problem statement, all variables and given/known data

    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?

    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Dec 3, 2012 #2

    Dick

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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.
     
  4. Dec 3, 2012 #3
    Why are the m vectors in R^n?
     
  5. Dec 3, 2012 #4

    Dick

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    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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