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October 9th, 2015, 11:59 AM   #1
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Reduced Row Echelon Form is Unique Proof

Let R1 and R2 be reduced row echelon forms of A. Then
R1<->R2 by elementary row operations.

Therefore:
R1 and R2 have same number of non-zero rows, same location of the (0,..0,1,0,..0)columns, and same elements in the non-zero rows.

Examples

$\displaystyle \begin{vmatrix}
1 &0 & 2 &1 \\
0 & 1&3 &5 \\
0 &0 & 0 & 0
\end{vmatrix} and\begin{vmatrix}
1 &4 &0 &0 \\
0& 0 &1 &0 \\
0 &0 &0 &1
\end{vmatrix}$


$\displaystyle \begin{vmatrix}
1 &0 & 2 &5 \\
0 & 1&7 &2 \\
0 &0 & 0 & 0
\end{vmatrix} and\begin{vmatrix}
1 &0 &4 &6 \\
0& 1 &1 &3 \\
0 &0 &0 &0
\end{vmatrix}$
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