Calculus
Jacobian Matrix
Consider the function \(f: \mathbb{R}^2\to \mathbb{R}^2\) defined by \(\cv{x\\y}\mapsto \cv{3\,y-3\,x \\ x^2+y^2}\).
Compute the Jacobian matrix \(J(x,y)\) and determine its value in the point \((x,y)=(0,-1)\).
| \(J(x,y) ={}\) |
| \(J(x,y)\Biggl|_{(0,-1)} ={}\) |
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