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Math Help - column/row space and RREF

  1. #1
    Senior Member I-Think's Avatar
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    column/row space and RREF

    The column space and the row space of a matrix is the span of all its columns and the span of all its rows respectively. Is it true that the column
    space of a matrix equals the column space of its RREF? Or the the row space of
    a matrix equals the row space of its RREF?


    Need a few hints to begin please?
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  2. #2
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    Is it true that the column space of a matrix equals the column space of its RREF?
    No. Row operations change the column space.

    Or the the row space of a matrix equals the row space of its RREF?
    Yes. Row space is unaffected by row operations.
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