Show that $col(A^T) = col(C^T)$, where $C$ is the matrix resulting from any number of row operations on $A$. I was given the hint that $A^T = C^T (P^{−1})^T$, but I don't see how I can conclude anything from that.
Show that row operations leave column space of transpose unchanged?
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linear-algebra
vector-spaces
gaussian-elimination
transpose
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0Do you have the result that the row space is preserved by row operations? – 2017-02-09
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0Unfortunately we haven't talked about the row space in lecture yet. I think I need to use the hint given to show equality. – 2017-02-09