# Thread: Row Reducing with a Variable

1. ## 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

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

2. 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

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

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

3. thank you thank you thank you!