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Math Help - Linear independence of row vectors

  1. #1
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    Linear independence of row vectors

    If A and B are row equivalent matrices, then the row vectors of A are linearly independent iff the row vectors of B are linearly independent. How exactly do you prove this?

    This is my thought so far: First we assume the row vectors of A are linearly independent, hence they form a basis for the rowspace of A. Now since elementary row operations do not change the rowspace of a matrix, then the row vectors of B span the same space. So the row vectors of A also form a basis for the rowspace of B.
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  2. #2
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    Re: Linear independence of row vectors

    Sounds good to me.
    Thanks from usagi_killer
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