Let f(x,y)=x2exyf(x, y) = x^2e^{xy}f(x,y)=x2exy. Find the Hessian matrix HfH_fHf at the point (1,0)(1, 0)(1,0).
(2221)\begin{pmatrix} 2 & 2 \\ 2 & 1 \end{pmatrix}(2221)
(2110)\begin{pmatrix} 2 & 1 \\ 1 & 0 \end{pmatrix}(2110)
(2331)\begin{pmatrix} 2 & 3 \\ 3 & 1 \end{pmatrix}(2331)
(0221)\begin{pmatrix} 0 & 2 \\ 2 & 1 \end{pmatrix}(0221)