Quadratic Forms


by stunner5000pt
Tags: forms, quadratic
stunner5000pt
stunner5000pt is offline
#1
Apr7-06, 04:31 PM
P: 1,445
Write the equation in terms of new caraibles so that it is in standard position and identify the curve

[tex] 3x^2 - 4xy = 2 [/tex]

here a = 3, b = -4, c = 0 , [tex] d = \sqrt{(-4)^2+(3-0)^2} = 5 [/itex]

[tex] \cos\theta = \frac{a+c-d}{\sqrt{b^2 + (a+c-d)^2}} = \frac{-2}{2\sqrt{5}} [/tex]
[tex] \sin\theta = \frac{b}{\sqrt{b^2 + (a+c-d)^2}} = \frac{4}{\sqrt{20}} [/tex]

so [tex] P = \frac{1}{\sqrt{5}} \left(\begin{array}{cc} -1&-2 \\ 2&-1 \end{array}\right) [/tex]

from X = PY i get
[tex] x = \frac{-1}{\sqrt{5}} (x_{1}-2y_{1}) [/tex]
[tex] y = \frac{-1}{\sqrt{5}} (2x_{1}+y_{1}) [/tex]
where x1 and y1 are the new variables
is this fine??

is this how you get the change of variables??
Phys.Org News Partner Science news on Phys.org
SensaBubble: It's a bubble, but not as we know it (w/ video)
The hemihelix: Scientists discover a new shape using rubber bands (w/ video)
Microbes provide insights into evolution of human language

Register to reply

Related Discussions
matrix forms of quadratic equations Precalculus Mathematics Homework 4
Quadratic forms Calculus & Beyond Homework 3
quadratic forms of symmetric matrices Linear & Abstract Algebra 6
binary quadratic forms Linear & Abstract Algebra 11
Quadratic forms, linear algebra Introductory Physics Homework 3