Simplified forms of Maxwell's curl equations for special case of $vec{J}$

From Maxwell’s curl equations, obtain the particular differential equations for the case of
$vec{J} = J_z(y,t)hat{z}$.

The solution provided for this question shows something like this:

$begin{vmatrix}
vec{a_x}&vec{a_y}&vec{a_z}
0&frac{partial}{partial y}&0
{E_x}&{E_y}&{E_z}
end{vmatrix} = -frac{partial vec{B}}{partial t}$ and
$begin{vmatrix}
vec{a_x}&vec{a_y}&vec{a_z}
0&frac{partial}{partial y}&0
{H_x}&{H_y}&{H_z}
end{vmatrix} = vec{J}+frac{partial vec{D}}{partial t}$

Why does the $nabla$ have components with 0 value?