Step 1:
The curl of a vector field $\mathbf{F}$ is given by the determinant of the following matrix:
$$\nabla \times \mathbf{F}=\left|\begin{array}{ccc}
\mathbf{i} & \mathbf{j} & \mathbf{k} \\
\frac{\partial}{\partial x} & \frac{\partial}{\partial y} &
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