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snu
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I am studying the subject of linear dependence right now and had a question on this topic. Is it possible to construct a square matrix A such that the columns of A are linearly dependent, but the columns of the transpose of A are linearly independent? My intuition tells me no, but I'm not sure how I would prove this to be the case in general. I've tried constructing several square matrices that are linearly dependent and taken the transpose and found that to be linearly dependent as well, but I'm not sure if this always holds.