Jacobian Matrix

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

Compute the Jacobian matrix $J(x,y)$ and determine its value in the point $(x,y)=(-3,-1)$ .

$J(x,y) ={}$

$\matrix{\Box & \Box \\ \Box & \Box}$

$J(x,y)\Biggl|_{(-3,-1)} ={}$

$\matrix{\Box & \Box \\ \Box & \Box}$

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