A Jacobian Through a Dead ReLU

A tiny two-layer network maps $x \in \mathbb{R}^2$ to $y \in \mathbb{R}^2$:

$z = W_1 x, \qquad h = \mathrm{ReLU}(z) \ \text{(elementwise)}, \qquad y = W_2 h$

with

$W_1 = \begin{pmatrix}1 & -1\\ 2 & 1\\ 0 & 3\end{pmatrix} \ (3\times2), \qquad W_2 = \begin{pmatrix}1 & 2 & -1\\ 0 & 1 & 1\end{pmatrix} \ (2\times3)$

Evaluate at the input $x = \begin{pmatrix}1\\ 2\end{pmatrix}$.

Find the Jacobian $J = \dfrac{\partial y}{\partial x}$ at this $x$, and use it to give the first-order change in the output for the small input perturbation $\delta = \begin{pmatrix}0.1\\ -0.1\end{pmatrix}$.