Mathematik-Online problems: Problem 64: ENF and Type of Quadrics

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	Mathematik-Online problems:
	Problem 64: ENF and Type 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

Find the Euclidean normal form of the following quadrics and determine their types:

a): ${\displaystyle{Q_1:\, -\frac{3}{8}\,x_1^2+\frac{1}{9}\,x_2^2-\frac{3}{8}\,x_3^2+\frac{5}{4}\,x_1x_3+\sqrt{2} x_1+\frac{2}{9}\,x_2-\sqrt{2} x_3+\frac{1}{9} = 0}}$
b): ${\displaystyle{Q_2:\, x_1^2+x_2^2+4x_3^2+6x_1x_2+12x_1x_3+4x_2x_3+8x_1+4x_2-2x_3+10 = 0}}$
c): ${\displaystyle{Q_3:\, 3x_1^2+3x_2^2+6x_3^2+2x_1x_2+4x_1x_3-4x_2x_3+2x_1+2x_2-2x_3+1 = 0}}$

(Authors: Kimmerle/Roggenkamp/Apprich/Höfert)

Solution:

automatisch erstellt am 14. 12. 2007