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Quadratic Form and matrices question

  1. Feb 20, 2010 #1
    1. The problem statement, all variables and given/known data

    Find the matrix that represents the given quadratic form relative to the variables yi.
    a) [tex] q(x_1, x_2, x_3) = 4x_1x_2 - 2x_1x_3 + {x_2}^2 +2x_3x_2 [/tex]

    [tex] x_1 = y_1 [/tex]
    [tex] x_2 = -y_1 + y_2 + 2y_3 [/tex]
    [tex] x_3 = -y_1 + 2y_2 + 2y_3 [/tex]

    2. Relevant equations

    3. The attempt at a solution

    Can I get the change of basis matrix P from B to standard R3 basis from this stuff

    [tex] x_1 = y_1 [/tex]
    [tex] x_2 = -y_1 + y_2 + 2y_3 [/tex]
    [tex] x_3 = -y_1 + 2y_2 + 2y_3 [/tex]


    From doing this PY = X to get P?

    And then I can do the whole YTPTAPY thing and get the matrix it's asking for?
  2. jcsd
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