Mathematik-Online problems: Problem 181: Diagonalization of Quadrics

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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

, so that $T^{-1}AT$ is diagonal.

b)

Find the normal form of the quadric

and sketch it in normal form coordinates. Find the center of

. Find all lines passing through the point $P(0, \frac{1}{2}, 1)$ and which are totaly contained in

(Authors: NN/Höfert)

Solution:

automatisch erstellt am 14. 12. 2007