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Matrix of a quadratic form

  1. Nov 7, 2011 #1
    1. The problem statement, all variables and given/known data
    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.

    3. 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?
    Last edited: Nov 7, 2011
  2. jcsd
  3. Nov 7, 2011 #2
    my book does not explain anything... Can anyone recommend a good one?
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