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How do I calculate the column rank of the matrix: $$\begin{bmatrix} -2 & -4 & -6 & 0 \\ 0 & -12 & 24 & 0 \\ 0 & 0 & 28 & -4 \\ 0 & 0 & 0 & 0\end{bmatrix}$$

I initially thought it would be $3$ as there are $3$ pivots. But then I realized that it will give me the row rank. Is that correct? If yes, then how do I calculate the column rank using pivots or otherwise?

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  • $\begingroup$ This depends on your field. Over the field $\Bbb F_2$ this is the zero matrix. Over a field of characteristic zero, the rank is obviously $3$, because column rank equals the row rank - see this duplicate for example. $\endgroup$ Commented Mar 17, 2023 at 17:06
  • $\begingroup$ @DietrichBurde I was considering $\mathbb{R}$ as the field. $\endgroup$
    – supremacy
    Commented Mar 17, 2023 at 19:36

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