Quadric surface question, given 3x3 matrix A and (x^T)Ax=6

In summary, the conversation discusses understanding and solving a problem involving matrix A and matrix multiplication. The solution involves multiplying the first number in matrix A by its position in the matrix, and repeating for all numbers in the matrix. The individual seems to have a good understanding and has referred to their course manual for help. They confirm that the solution involves matrix multiplication and thanks the other person for their help.
  • #1
imsleepy
49
0
BTXGF.jpg


this is my working out:

http://i.imgur.com/1hsQS.jpg

i sort of figured out how to do this a few mins ago lol. it doesn't seem too hard.
it's sort of like... multiplying the first number in the matrix A by it's position in the matrix (x1 * x1) which is basically the coordinates of the value, then doing that for all numbers in the matrix A.

am i right? have i fully answered the question?

edit: in my working out, the xTAx = sigma sigma axx was taken from my course manual.
 
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  • #2
haven't followed it all through, but i think you have the right idea

the sigma sigma is just matrix multiplication
 
  • #3
awesome, thank you :)
 

1. What is a quadric surface?

A quadric surface is a type of three-dimensional surface that can be described by a second-degree equation, such as (x^T)Ax=6. It is a generalization of conic sections in two dimensions and can have various shapes, including ellipsoids, hyperboloids, and paraboloids.

2. What is the significance of the 3x3 matrix A in the quadric surface equation?

The 3x3 matrix A determines the shape and orientation of the quadric surface. It contains the coefficients of the second-degree terms in the equation and can be used to classify the surface into different types.

3. How do you solve a quadric surface question given a 3x3 matrix A and (x^T)Ax=6?

To solve a quadric surface question, you can use matrix algebra and algebraic manipulation to find the values of x that satisfy the equation (x^T)Ax=6. This involves finding the eigenvalues and eigenvectors of the matrix A and using them to transform the equation into a simpler form.

4. What does the value 6 represent in the quadric surface equation (x^T)Ax=6?

The value 6 represents the constant term in the equation, which can be thought of as the height of the quadric surface above the xy-plane. It can also be interpreted as the level at which the surface intersects the z-axis.

5. Are there any real-world applications of quadric surfaces?

Yes, quadric surfaces have many real-world applications in fields such as engineering, physics, and computer graphics. They are used to model the shape of objects such as lenses, satellite dishes, and reflectors. They also play a role in optimization problems and computer vision algorithms.

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