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

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SUMMARY

The discussion centers on solving the equation (x^T)Ax=6 using a 3x3 matrix A. The participant describes their approach, which involves multiplying each element of matrix A by its corresponding position in the vector x, confirming that this method aligns with the principles of matrix multiplication. The reference to the equation x^T A x as sigma sigma axx indicates an understanding of the summation notation used in linear algebra. The participant expresses confidence in their solution process, suggesting they have grasped the core concepts involved.

PREREQUISITES
  • Understanding of linear algebra concepts, specifically matrix multiplication.
  • Familiarity with quadratic forms and their representation in matrix notation.
  • Knowledge of summation notation and its application in mathematical equations.
  • Basic proficiency in manipulating 3x3 matrices.
NEXT STEPS
  • Study the properties of quadratic forms in linear algebra.
  • Learn about eigenvalues and eigenvectors related to 3x3 matrices.
  • Explore applications of matrix multiplication in solving systems of equations.
  • Investigate the geometric interpretation of quadric surfaces defined by quadratic forms.
USEFUL FOR

Students and professionals in mathematics, particularly those studying linear algebra, as well as anyone interested in understanding the applications of quadratic forms in various fields such as physics and engineering.

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

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

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