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Subspace of A and a matrix formed by row operation

  1. Jul 5, 2010 #1
    The subspace formed by matrix A and A' will be same or different if A' is obtained by applying an elementary row operation on A?
    Please prove it.
     
  2. jcsd
  3. Jul 5, 2010 #2

    HallsofIvy

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    In what sense does a matrix or two matrices "form" a subspace?

    Are you referring to the subspace of [itex]M_{mxn}[/itex] of m by n matrics spanned by two such matrices?
     
  4. Jul 5, 2010 #3
    Sorry sir i used wrong word.
    i meant spanned by two matrices A and A'.
     
  5. Jul 5, 2010 #4

    Office_Shredder

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    Different compared to what? If you apply a different elementary row operation?
     
  6. Jul 5, 2010 #5
    I mean sir Col A = Col A'
    Is it true or not.
     
  7. Jul 6, 2010 #6

    Office_Shredder

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    Hah, now that that's cleared up.

    What have you tried so far? It might be a good idea to look at a couple of small examples (2x2 or 2x3 matrices) just to see what's going on (especially because you don't know if the statement is true, so you might find a counterexample)
     
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