# Row Reducing with a Variable

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• July 22nd 2009, 02:31 PM
Zocken
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?
• July 22nd 2009, 08:28 PM
CaptainBlack
Quote:

Originally Posted by Zocken
$\begin{array}{cccc}2&a&2&0\\0&2&a&2\\0&0&2&a\\a&2& 0&0\end{array}$

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:

$\begin{array}{cccc}
2&a&2&0\\
0&2&a&2\\
0&0&2&a\\
0&2-a^2/2&-a&0
\end{array}$

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

CB
• July 22nd 2009, 09:27 PM
Zocken
thank you thank you thank you!