Verify the identity (operatorname{div}(operatorname{curl} mathbf{F})=0) for the vector fields (mathbf{F}=leftlangle x z, y e^{x}, y zightangle) and
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Verify the identity \(\operatorname{div}(\operatorname{curl} \mathbf{F})=0\) for the vector fields \(\mathbf{F}=\left\langle x z, y e^{x}, y zightangle\) and \(\mathbf{G}=\left\langle z^{2}, x y^{3}, x^{2} yightangle\).
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