(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Consider the quadratic form

q(v) = x_{1}^{2}+ 5x_{2}^{2}+ 11x_{3}^{2}+ 4x_{1}x_{2}+ 6x_{1}x_{3}+ 14x_{2}_{3}

Relative to the standard basis of R3 find the symmetric matrix A associated with q.

3. The attempt at a solution

In the standard basis, I'll use

e_{1}= [1,0,0]

e_{2}= [0,1,0]

e_{3}= [0,0,1]

if it were in R2, I would say [a_{ij}] = q(e_{i},e_{j}) but how do I do this in R3? and I only have 3 variables, so I have to only use one vector, but which entry in the matrix does each one represent?

How do I determine which vectors to use for with entries.

*edit* I'll just specify, if I wanted to find [a_{11}] I could just use q(e_{1}), but what about [a_{21}] for example?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Matrix of a quadratic form

**Physics Forums | Science Articles, Homework Help, Discussion**