7.3: Gauss Jordan Elimination and the Row Echelon Form
- Page ID
- 63902
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The above video left out a special case for Reduced Row Echelon form. There can be non-zero elements in columns that do not have a leading one. For example, All of the following are in Reduced Row Echelon form:
\[\begin{split}
\left[
\begin{matrix}
1 & 2 & 0 & 3 & 0 & 4 \\
0 & 0 & 1 & 2 & 0 & 7 \\
0 & 0 & 0 & 0 & 1 & 6 \\
0 & 0 & 0 & 0 & 0 & 0
\end{matrix}
\right]
\end{split} \nonumber \]
\[\begin{split}
\left[
\begin{matrix}
1 & 2 & 0 & 0 & 4 \\
0 & 0 & 1 & 0 & 6 \\
0 & 0 & 0 & 1 & 5
\end{matrix}
\right]
\end{split} \nonumber \]
What are the three steps in the Gauss-Jordan Elimination algorithm?