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Math Help - Row Reducing with a Variable

  1. #1
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    Row Reducing with a Variable

    \begin{array}{cccc}2&a&2&0\\0&2&a&2\\0&0&2&a\\a&2&  0&0\end{array}

    somehow reduces to

    \begin{array}{cccc}2&a&2&0\\0&2&a&2\\0&0&2&a\\0&0&  0&-2+(3/2)a^2-(1/8)a^4\end{array}

    Can someone explain please?
    Last edited by Zocken; July 22nd 2009 at 03:41 PM.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Zocken View Post
    \begin{array}{cccc}2&a&2&0\\0&2&a&2\\0&0&2&a\\a&2&  0&0\end{array}

    somehow reduces to

    \begin{array}{cccc}2&a&2&0\\0&2&a&2\\0&0&2&a\\0&0&  0&-2+(3/2)a^2-(1/8)a^4\end{array}

    Can someone explain please?
    Subtract a/2 times the first row from the fourth to get:

    \begin{array}{cccc}<br />
2&a&2&0\\<br />
0&2&a&2\\<br />
0&0&2&a\\<br />
0&2-a^2/2&-a&0<br />
\end{array}

    Now subtract 1-a^2/4 times the second row from the fourth, ...

    CB
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  3. #3
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    thank you thank you thank you!
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