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Math Help - Quadratic Forms - Reduction Techniques

  1. #1
    Junior Member ibnashraf's Avatar
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    Quadratic Forms - Reduction Techniques

    hi all,

    i am trying to do an assignment here and i would like to verify my answer to the following question:

    Let Q=x_1^2+2x_2^2-7x_3^2-4x_1x_2+8x_1x_3
    Find a non-singular matrix P and a diagonal matrix D=diag(d_1,d_2,d_3) such that Q is transformed to Q'=d_1y_1^2+d_2y_2^2+d_3y_3^2; under the transformation X=PY
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  2. #2
    Junior Member ibnashraf's Avatar
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    Re: Quadratic Forms - Reduction Techniques

    i used the congruence method of reduction and i ended up with

    D=diag(1, 4, -288)

    and P=\left(\begin{array}{ccc}1&0&-8\\0&4&28\\0&2&16\end{array}\right)

    Is my answer correct?
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