Is the matrix $$\begin{pmatrix} 0 & 0 & 0\\ 0 & 0 & 0\\ 0 & 0 & 0 \end{pmatrix}$$ In row echelon form? Or even the reduced row echelon form?

Thank you very much!

  • $\begingroup$ The key is to look at the definition you were given of (reduced) row echelon form, and see if it applies. The answer is yes. $\endgroup$ – vadim123 Oct 5 '17 at 22:05
  • $\begingroup$ @vadim123 Thank you very much! Yes, as this example does not include non-zero rows, so I am not certain whether the rule “if all rows containing only 0 are below all other rows” can be applied here. $\endgroup$ – Danny Oct 5 '17 at 22:08
  • $\begingroup$ Modify the rule to be "if all rows containing only 0 are below all other rows [assuming they exist in the first place]" $\endgroup$ – JMoravitz Oct 5 '17 at 22:23

Yes it is.

Think of it this way: if it wasn't, then there would have to be a non-zero row in the matrix, which would prevent the matrix from being in RREF. Since there is no such non-zero row, you can conclude that the matrix is indeed in RREF.

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  • $\begingroup$ Got that! Thank you very much^_^ $\endgroup$ – Danny Oct 6 '17 at 0:48
  • $\begingroup$ @DannyC If this answer is enough for you to "get it" then don't forget to accept it. $\endgroup$ – drhab Oct 11 '17 at 9:18
  • $\begingroup$ @drhab Yes! Could you tell me how to accept it. I was new to this forum^_^ lol $\endgroup$ – Danny Oct 11 '17 at 9:21
  • $\begingroup$ On the upper left corner (right under the $0$ right now) move with your mouse. Then you find an option for acceptance there too, exactly under the option for downvoting. $\endgroup$ – drhab Oct 11 '17 at 9:25

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