Summing Quadratic Forms in Three Variables: True or False?

[MikeDietrich]

Homework Statement

True or False and Why?

"The sum of two quadratic forms in three variables must be a quadratic form as well."

Homework Equations

q(x_1,x_2,x_3)=x_1^2+x_2^2+x_3^2+x_1x_3+x_2x_3

The Attempt at a Solution

I am definitely missing something. To me this is a "duh" statement (and I am sure it's not). If I sum two equations in quadratic form then naturally the answer will be in the quadratic form. Any hints appreciated.

 

[micromass]

Yes, the answer looks quite trivial...

 

[statdad]

Are you dealing with quadratic forms associated with matrices?

$$x' A x$$

If so, you probably need to take that into account.