Matrix math help

[Kirby]

So I got a general equation of a quadratic equation:

Ax^2 + By^2 + Cz^2 + Dxy + Exz + Fyz + Gx + Hy + Iz + J = 0

And I need to make an augmented matrix with 9 points to find the coefficients(A, B, C, etc).

I know how to do it for 2 dimensions, first column is 1, second is the x's, the second is x^2, and the last is y, then you just make it to a reduced echelon form, and you got all the coefficients.

But I have no clue how to form the augmented matrix in 3D.

Halp?

 

[NoReMoRsE]

There is no spoon.

 

[venkman]

Originally posted by: NoReMoRsE
There is no spoon.

obvious joke in first reply. I love atot.

 

[Kirby]

Bump for the Night/Early morning Crew!

 

[Kirby]

Bueller?

 

[Fenixgoon]

i'm not sure, but is there any reason why you couldn't make a 3 dimensional matrix? 3x3x3?

 

[Cawchy87]

Is that what the question states exactly? Cause it can be translated/rotated to one of two standard forms. I vaguely remember this stuff from my muli-variable calc course a few years ago.

 

[Kirby]

Question: The general equation of a quadratic surface is: Ax^2 + By^2 + Cz^2 + Dxy + Exz + Fyz + Gx + Hy + Iz + J = 0.

Consider the quadratic surface that contains the following points: (1,2,3) (2,1,0), etc. (there are 9 points).

(a) Implement the augmented matrix S of the system that determines the coefficients A through J of the equation of the surface.

(b) Key in an equation of the surface.

We haven't done 3d matrices, and i would hope he wouldn't have a Matlab lab that would include it.

 

[Cawchy87]

Sorry bud, it's been too long for me. Good luck with it. What are you taking in school?

 

[Kirby]

Originally posted by: Cawchy87
Sorry bud, it's been too long for me. Good luck with it. What are you taking in school?

I'm a CS major, and this is for my Applied Matrix Theory math class. This is the last question for the lab, and I've been searching like hell for a hint.

 

[Cawchy87]

Ah, I took this stuff in a different course not concentrating on matrices and only using them when necessary (jacobian etc.). Wish I could help ya out. Look up the guru's who help on other math threads, they might be able to help you out.

 

[Kirby]

I think I got it. If I put it into the equation into reduced echelon form, I get A through I in terms of J. Then put it back into the equation, substituting A-I with J, then divide out J. So now I've got coefficients with all of the x,y,z's.