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Is there a way to visualize the action of elementary matrices? (Or perhaps matrices in general). Perhaps someone could give an intuitive view of the effects of elementary row operations.

Actually I am trying to intuitively understand why these elementary matrices general $GL_n$.

Thanks.

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    The $i$-th column of a matrix $A$ shows you what $A$ will do to the $i$-th unit vector. Knowing this it should be easy to see what geometric operation your elementary matrices represent.2011-11-05

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