I have the following quadratic equation:
$$2xy + 2xz - 6x - 6y - 4z = -9.$$
How do I put this kind of equation in matrix form? This is a two‐sheeted hyperboloid.
I've learned how to convert equations like hyperboloid to matrix form: $$ax^2+by^2-cxy=1$$
By setting "a"and "b" in the main diagonal and splitting c in the antidiagonal yielding a symmetric matrix. Similar to R3 equations.
However this equation has no squared variables, so I'm a bit lost.
Any help is appreciated. Thx.
Since there are no squared variables, your matrix will have zeros on the diagonal.
Also, forget about the linear terms to begin with; they don't enter into the matrix. After rotating the coordinate system (so that the axes point in the directions of the eigenvectors of the matrix), you can complete the squares to get rid of the linear terms.