Consider the quadratic form
q(v) = x12 + 5x22 + 11x32 + 4x1x2 + 6x1x3 + 14x23
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
e1 = [1,0,0]
e2 = [0,1,0]
e3 = [0,0,1]
if it were in R2, I would say [aij] = q(ei,ej) 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 [a11] I could just use q(e1), but what about [a21] for example?