# Echelon form for a $2\times 2$ matrix

So I'm to describe the possible forms of a $2\times 2$ matrix in Echelon form. I thought the only way we could have a $2\times 2$ matrix in Echelon form is like this: $$\left[\begin{matrix}1&c\\ 0&0\end{matrix}\right]$$ Where $c$ is just some constant. But I'm told that we can have it in the form $$\left[\begin{matrix}1&c\\0&1\end{matrix}\right]$$ and $$\left[\begin{matrix}0&1\\0&0\end{matrix}\right]$$But how come we can have a leading entry in the last column when this just leaves the matrix inconsistent? Is it because consistency doesn't matter when it comes to just classifying a matrix as "in Echelon form"?

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+1 For a $2\times 2$ matrix it is done too fast, but for higher it takes time. –  Babak S. Feb 5 '13 at 3:49