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Mathematik-Online problems:

Problem 181: Diagonalization of Quadrics


A B C D E F G H I J K L M N O P Q R S T U V W X Y Z


a)
Given the matrix

$\displaystyle A=\left(\begin{array}{rrr} 0 & -1 & 1 \\ -1 & 0 & -1 \\ 1 & -1 & 0
\end{array}\right). $


Find an orthogonal matrix $ T$ , so that $ T^{-1}AT$ is diagonal.
b)
Find the normal form of the quadric $ Q: -2x_1x_2+2x_1x_3-2x_2x_3+1=0$ and sketch it in normal form coordinates. Find the center of $ Q$ . Find all lines passing through the point $ P(0, \frac{1}{2}, 1)$ and which are totaly contained in $ Q$ .

(Authors: NN/Höfert)

see also:


[Solutions]

  automatisch erstellt am 14. 12. 2007