Three Layers, One Matrix, One Zero

A network stacks three fully connected layers with no activation function anywhere — every layer is a plain affine map:

$\mathbf{h}_1 = W_1\mathbf{x} + \mathbf{b}_1, \qquad \mathbf{h}_2 = W_2\mathbf{h}_1 + \mathbf{b}_2, \qquad \mathbf{y} = W_3\mathbf{h}_2 + \mathbf{b}_3$

with

$W_1 = \begin{bmatrix} 1 & 2 \\ 0 & 1 \end{bmatrix}, \qquad W_2 = \begin{bmatrix} 2 & -1 \\ 1 & 1 \end{bmatrix}, \qquad W_3 = \begin{bmatrix} 2 & 1 \\ 0 & -1 \end{bmatrix}$

$\mathbf{b}_1 = \begin{bmatrix} 1 \\ -1 \end{bmatrix}, \qquad \mathbf{b}_2 = \begin{bmatrix} 0 \\ 2 \end{bmatrix}, \qquad \mathbf{b}_3 = \begin{bmatrix} 3 \\ 0 \end{bmatrix}$

Because nothing nonlinear sits between the layers, the entire stack is equivalent to a single affine map

$\mathbf{y} = M\mathbf{x} + \mathbf{c}$

that produces identical outputs for every input $\mathbf{x} = (x_1,\ x_2)$.

Exactly one input makes this network output the zero vector, $\mathbf{y} = (0,\ 0)$.

For that input, what is $x_2$? Round your answer to 3 decimal places.