Form signature from its expression

Task number: 2741

Determine the signature of the real quadratic form \(g\) with the following analytic expression:

  • Variant

    \(g((x,y,z)^T)=-2xy+2xz+y^2-z^2\)

  • Variant

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

  • Variant

    \(g((x_1, x_2, x_3, x_4)^T) = 2x_1^2 + 2x_1x_2 - x_2^2 - 2x_2x_4 - x_4^2\)
  • Variant

    \(g((x_1, x_2, x_3, x_4)^T) = x_1x_2 + x_1x_3 + x_1x_4 + x_2x_3 + x_2x_4 + x_3x_4\)
  • Variant

    \(g((x_1, x_2, x_3, x_4)^T) = x_1^2 + 2x_2^2 + x_4^2 + 4x_1x_2 + 4x_1x_3 + 2x_1x_4 + 2x_2x_3 + 2x_2x_4 + 2x_3x_4\)
Difficulty level: Moderate task
Routine calculation training
Cs translation
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