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    Hi guys, just a quick question on terminology.
    For a matrix to be in row echelon form does the leading coefficient of each non zero row have to be 1. Im pretty certain its does, otherwise it would simply be classified as an upper triangular matrix, that is if its a square matrix.
    I ask becauce there seems to be on the Gaussian Elimination page of wikipedia (yes I know wikipedia is certainly not the best place to be learning maths from, but I was just flicking through and saw this ) a description of this augmented matrix

    \left[ \begin{array}{ccc|c}

2 & 1 & -1 & 8 \\

0 & \frac{1}{2} & \frac{1}{2} & 1 \\

0 & 0 & -1 & 1 

\end{array} \right]

    as being in row echelon form, but to me thats just in upper triangular. Or rather the unaugmented matrix of coefficients is in upper triangular form, so would the augmented matrix even have a 'special' name. Thanks alot guys ;D
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    what would you classify this matrix as?

    0 X X
    0 0 X
    0 0 0

    or

    0 X X
    0 0 0
    0 0 0

    where the Xs are different numbers (not 0).
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    emmm ha, well the first I would say is a strictly upper triangular matrix, but (as far as I know as I still dont know the answer to my question ) it 'could' also be in row echelon form if the leading coeffiecients are 1, and the second, same it 'could' be in row echelon form.

    Thanks for the post idun, not that I dont appeciate it or anything, I just still am not any closer to answer my question
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    (Original post by Galadirith)
    Hi guys, just a quick question on terminology.
    For a matrix to be in row echelon form does the leading coefficient of each non zero row have to be 1.
    It hardly matters, surely?

    The honest answer is probably that everyone's definitions are different. It really doesn't matter because once you're in upper triangular form, you can always very easily force the main diagonal to be made of 1s, after which you can put it into reduced form and get everything above the main diagonal to be zero.
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    Thank generalebriety , sure you are absolutly right, I suppose in the grand scheme of things it doesnt really matter, it was more my curiosity getting the better of me, thanks for the post guys.
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    (Original post by Galadirith)
    Thank generalebriety , sure you are absolutly right, I suppose in the grand scheme of things it doesnt really matter, it was more my curiosity getting the better of me, thanks for the post guys.
    Ah, don't see my post as dismissive. The point is that maths isn't all set in stone; people's definitions, notation, etc. vary (I've seen plenty of crazy definitions / notation) according to what they find most useful. Here, "row echelon form" is just a useful label for "a form that will allow us to do the things that row echelon form should allow us to do", which can be either of the above forms.
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    (Original post by Galadirith)
    Hi guys, just a quick question on terminology.
    For a matrix to be in row echelon form does the leading coefficient of each non zero row have to be 1. Im pretty certain its does, otherwise it would simply be classified as an upper triangular matrix, that is if its a square matrix.
    No. For example

    \left( \begin{array}{ccc}

0 & 0 & 1 \\

0 & 1 & 0 \\

0 & 0 & 1 \end{array} \right)

    is upper triangular but not in row echelon form.
 
 
 
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