Signature of a form in R3

Task number: 2741

Determine the signature of the quadratic form \(g\) on \(\mathbb R^3\), that for \(u=(x, y, z)^T\) has the following analytic expression

  • Variant 1

    \(g(u)=-2xy+2xz+y^2-z^2\).

  • Variant 2

    \(g(u)=x^2+6xy+4xz+9y^2+12yz+4z^2\).

Difficulty level: Moderate task
Routine calculation training
Cs translation
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