7.3: Gauss Jordan Elimination and the Row Echelon Form

Matrix Algebra with Computational Applications · LibreTexts

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    From LibreTexts, under CC BY-NC 4.0, as the source states it; its equations are written in TeX, which the PDF shows typeset. This page at LibreTexts.

    from IPython.display import YouTubeVideo
YouTubeVideo("v6RstFsrTJY",width=640,height=360, cc_load_policy=True)

    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:

    \[\begin{split}
    \left[
    \begin{matrix}
    1 & 2 & 0 & 3 & 0 & 4 \\
    0 & 0 & 1 & 2 & 0 & 7 \\
    0 & 0 & 0 & 0 & 1 & 6 \\
    0 & 0 & 0 & 0 & 0 & 0
    \end{matrix}
    \right]
    \end{split} \nonumber \]

    \[\begin{split}
    \left[
    \begin{matrix}
    1 & 2 & 0 & 0 & 4 \\
    0 & 0 & 1 & 0 & 6 \\
    0 & 0 & 0 & 1 & 5
    \end{matrix}
    \right]
    \end{split} \nonumber \]

    Question

    What are the three steps in the Gauss-Jordan Elimination algorithm?

    This page titled 7.3: Gauss Jordan Elimination and the Row Echelon Form was last modified on Sat, 17 Sep 2022 15:14:24 GMT and is shared under a CC BY-NC 4.0 license and was authored, remixed, and/or curated by Dirk Colbry via source content that was edited to the style and standards of the LibreTexts platform.