# Example of Matrix in Reduced Row Echelon Form

I'm struggling with this question and can't seem to come up with an example:

Give an example of a linear system (augmented matrix form) that has:

• reduced row echelon form
• consistent
• 3 equations
• 1 pivot variable
• 1 free variable

The constraints that I'm struggling with is: If the system has 3 equations, that means the matrix must have at least 3 non-zero rows. And given everything else, how can I have only 1 pivot?

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if I only have 2 columns then I still don't see how I can have 3 pivots and satisfy the reduced row echelon form. The book that we're using states that a) if a row does not consist entirely of zeroes, then the first nonzero number in the row is a 1. If I have all 1s there it also can't be in the reduced echelon form because b) column with leading 1 must have 0 everywhere else .. $$\left[\begin{array}{rrr|r} 1 & * \\ 1 & * \\ 1 & * \end{array}\right]$$ Also, wouldn't this be just 1 variable in total? – user59547 Jan 25 '13 at 5:15
It counts as the equation $0x + 0y + ... = 0$. I know it sounds silly, but that's going to be what it means. On that note, I actually made a mistake (which I will now fix), as I didn't see that they were asking for an augmented matrix, in which case you need to throw in one more column. – Christopher A. Wong Jan 25 '13 at 8:48