Show that the vector field \( \mathbf{F}(x, y) = xy\mathbf{i} - x^{2}y\mathbf{j} \) is not conservative.
vector-fieldsconservative-vector-fieldspartial-derivativescross-partial-testmultivariable-calculusclairauts-theoremgradient-fields2d-vector-fieldscalculus-iiievaluate-conservativeprove-non-conservativecomponent-test
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