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## Homework Statement

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.

## 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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