(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?

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# Homework Help: Matrix of a quadratic form

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