# Is this a matrix of row echelon form? Or even the reduced row echelon form?

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!

• 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. – vadim123 Oct 5 '17 at 22:05
• @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. – Danny Oct 5 '17 at 22:08
• Modify the rule to be "if all rows containing only 0 are below all other rows [assuming they exist in the first place]" – 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.

• Got that! Thank you very much^_^ – Danny Oct 6 '17 at 0:48
• @DannyC If this answer is enough for you to "get it" then don't forget to accept it. – drhab Oct 11 '17 at 9:18
• @drhab Yes! Could you tell me how to accept it. I was new to this forum^_^ lol – Danny Oct 11 '17 at 9:21
• 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. – drhab Oct 11 '17 at 9:25