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

• imsleepy
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.
imsleepy

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.

haven't followed it all through, but i think you have the right idea

the sigma sigma is just matrix multiplication

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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