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Matrix of a quadratic form

  • Thread starter Locoism
  • Start date
  • #1
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Homework Statement


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?
 
Last edited:

Answers and Replies

  • #2
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my book does not explain anything... Can anyone recommend a good one?
 

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