Quadratic forms

[Filip84]

Show that the general equation of a quadratic surface in 3 dimensional euclidian space,
X'AX+BX+k=0
can be reduced to the form Y'AY=c if A is nonsingular.

Can someboy help me to solve the problem?

 

[stapel]

Show that the general equation of a quadratic surface in 3 dimensional euclidian space, X'AX+BX+k=0, can be reduced to the form Y'AY=c if A is nonsingular.

Would it be correct to assume that A, B, c, k, X, X', Y, and Y' are matrices? If so, what is the relationship between X and X', and between Y and Y', if any? Thank you. :wink:

 

[HallsofIvy]

And why do you only want boys to respond?

More seriously, I presume that \(\displaystyle X= \begin{bmatrix}x \\ y \\ z\end{bmatrix}\) and \(\displaystyle X'= \begin{bmatrix}x & y & z\end{bmatrix}\).

Hint: if this were in one dimension, you would complete the square.