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Math Help - Matrices - Elimination

  1. #1
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    Matrices - Elimination

    Hi,
    What is the difference between elementary row operations, Gaussian Elimination, and Gauss-Jordan Elimination?
    I am confused between these 3 concepts.

    For operations on rows on augmented matrices using elem. row operations, they said:
    1. Multiply a row through by a nonzero constant
    2. Interchange 2 rows
    3. Add a multiple of one row to another
    Their example wasn't clear to me though, so I don't understand the steps for that.
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  2. #2
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    Elementary Row Operations: Gaussian Elemination

    \displaystyle\begin{bmatrix}5&7\\1&12\end{bmatrix}  \Rightarrow\mbox{Change row 1 with 2}\begin{bmatrix}1&12\\5&7\end{bmatrix}\Rightarrow  \mbox{-5R1+R2}\begin{bmatrix}1&12\\0&-53\end{bmatrix}\Rightarrow\mbox{1/-53*R2}\begin{bmatrix}1&12\\0&1\end{bmatrix}

    Get the idea?
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  3. #3
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    Gauss Jordan

    \displaystyle\begin{bmatrix}1&12\\0&1\end{bmatrix}  \Rightarrow\mbox{R1-12R2}\begin{bmatrix}1&0\\0&1\end{bmatrix}
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  4. #4
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    Thanks.
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