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Mathematics-Online problems:

Interactive Problem 37: Normal Form of a Quadric

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
Given a quadric $ Q$ defined by

$\displaystyle 48x_1^2-33x_2^2-15x_3^2-120x_1x_2+48x_1x_3+48x_2x_3+434x_1-1504x_2+718x_3 = 1341\,. $

Bring the equation into matrix form

$\displaystyle x^{\operatorname t}Ax+2a^{\operatorname t}x+c=0\,. $

$ A= \left(\rule{0pt}{6ex}\right.$
$ \left.\rule{0pt}{6ex}\right)$

$ a= \left(\rule{0pt}{6ex}\right.$
$ \left.\rule{0pt}{6ex}\right)$

$ c=$

Determine the type of the quadric $ Q$ .

n/a
conic quadric
central quadric
parabolic quadric

Find the normal form of the quadric $ Q$ .

n/a
$ \frac{x_1^2}{a_1^2}+\frac{x_2^2}{a_2^2}=0$
$ \frac{x_1^2}{a_1^2}-\frac{x_2^2}{a_2^2}=0$
$ \frac{x_1^2}{a_1^2}+\frac{x_2^2}{a_2^2}+1=0$
$ \frac{x_1^2}{a_1^2}-\frac{x_2^2}{a_2^2}+1=0$
- $ \frac{x_1^2}{a_1^2}-\frac{x_2^2}{a_2^2}+1=0$
$ \frac{x_1^2}{a_1^2}-\frac{x_2^2}{a_2^2}+2x_3=0$

Give positive values $ 1/a_1$ and $ 1/a_2$ .

$ 1/a_1=$ $ \quad$ $ 1/a_2=$
   

(Authors: App/Höfert)
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  automatically generated: 8/11/2017