## Signature of a form in R3

Determine the signature of the quadratic form $$g$$ on $$\mathbb R^3$$, that for $$u=(x, y, z)^T$$ has the following analytic expression
$$g(u)=-2xy+2xz+y^2-z^2$$.
$$g(u)=x^2+6xy+4xz+9y^2+12yz+4z^2$$.