For $V = (V_1,V_2 )\in\mathbb{R}^2$ and $W = (W_1,W_2 )\in\mathbb{R}^2$ , Consider the determinant map $\det :\mathbb{R}^2 \times \mathbb{R}^2 \to \mathbb{R}$ defined by $\det(V,W) = V_1W_2 -V_2W_1$
Then the derivative of the determinant map at $(V,W)\in\mathbb{R}^2 \times \mathbb{R}^2$ evaluated on $(H, K )\in\mathbb{R}^2 \times\mathbb{R}^2$ is:
- $\det (H,W) + \det(V, K )$
- $\det (H, K )$
- $\det (H,V ) + \det(W, K )$
- $\det (V,W) + \det(K,W)$
Can anyone help me to solve this problem? Thank you.