Jacobian Matrix

Consider the function \(f: \mathbb{R}^2\to \mathbb{R}^2\) defined by \(\cv{x\\y}\mapsto \cv{-2\,x-y \\ -3\,x^2+y^2-2}\).

Compute the Jacobian matrix \(J(x,y)\) and determine its value in the point \((x,y)=(0,-2)\).

\(J(x,y) ={}\)

\(\matrix{\Box & \Box \\ \Box & \Box}\)

\(J(x,y)\Biggl|_{(0,-2)} ={}\)

\(\matrix{\Box & \Box \\ \Box & \Box}\)