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For an $m \times n$ matrix $A$ in row echelon form, $\mathrm{nullity} (A)$ is equal to the number of columns that do not contain a pivot. Is this also true for an infinite matrix in row echelon form with its origin in the lower right?

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  • $\begingroup$ I'm not sure I understand your question. My choice of the origin's position was somewhat arbitrary. It could also be the upper left, if you prefer. I don't see how one choice versus the other affects the result. By first column, do you mean the rightmost? $\endgroup$ Dec 1, 2019 at 16:48
  • $\begingroup$ If I have an infinite matrix with origin in the lower right, the 'leftmost' column is not defined. I don't see why upper-left and lower-right origin matrices are different in this context. If the origin is at the bottom right, there can be an infinite number of pivots above and to the left of it. $\endgroup$ Dec 1, 2019 at 17:06
  • $\begingroup$ Hmm, yes, I am sorry, I misread that. Self-deleting my comments soon. $\endgroup$ Dec 1, 2019 at 17:41

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