# Classification of Matrices

I need a little help on solving matrices. I actually just want to confirm my answer

Given matrices :

$$A= \begin{bmatrix} 2 & 0 & 8 & 9 & 7 \\ 0 & 0 & 1 & 2 & 3 \\ 0 & 0 & 0 & 7 & 6 \\ 1 & 0 & 0 & 0 & 9 \\ \end{bmatrix}$$

$$B= \begin{bmatrix} 2 & 0 & 8 & 9 & 7 \\ 0 & 0 & 1 & 2 & 3 \\ 0 & 0 & 0 & 7 & 6 \\ 0 & 0 & 0 & 0 & 9 \\ \end{bmatrix}$$

$$C= \begin{bmatrix} 2 & 0 & 8 & 9 & 7 \\ 0 & 0 & 1 & 2 & 3 \\ 0 & 0 & 0 & 1 & 6 \\ 0 & 0 & 0 & 0 & 1 \\ \end{bmatrix}$$

Which of the following are in reduced row echelon form ?

My answer is all the matrices are not in reduced row echelon form. Matrices B and C are in echelon form, but not matrix A.

Am I correct ?

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There is no need to write "solved" in the title; there is a green indicator on the questions that have an accepted answer. –  Zev Chonoles May 29 '13 at 5:21
Thank you Zev Chonoles for telling me that. I usually write SOLVED if the question is answered. Thank again Zev =) –  Garett May 29 '13 at 5:23
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## 1 Answer

What's the difference for you between echelon form (E.F.) and reduced E.F. (R.E.F.)? The latter must have $\,1'$s on the main diagonal or what?

If so then you're right: (b)-(c) are in E.F., none in R.E.F. (a) is not even triangular so not in E.F., either.

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echelon form in actually the gaussian elimination and row reduced echelon form is Gauss Jordan elimination. So my answer no problem right? because this is my assignment question –  Garett Jan 16 '13 at 18:11
Again, names say not much. Read carefully my answer about the 1's. If your defintiions are different then I can't say. –  DonAntonio Jan 16 '13 at 18:15
the one you said 1's on the main diagonal is R.E.F and E.F is the more zero proceed then the previous row –  Garett Jan 16 '13 at 18:17
I didn't understand your last words in the last comment, but it seems to be that: REF is the same as EF but with 1's on the main diagonal and these are the only non-zero entries in that column. So yes, your answer still holds. –  DonAntonio Jan 16 '13 at 18:21
Sorry I couldnt deliver what I trying to say to you. But what you said in the last comment is the one I trying to say. So again thank you very much DonAntonio for guiding me throughout the question. You really help me on my assignment.=) –  Garett Jan 16 '13 at 18:27
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