(Requires Appendix Material) a Necessary and Sufficient Condition to Derive $\sum _ { i = 1 } ^ { n } \hat { u } _ { i } = 0 \text { and } \sum _ { i = 1 } ^ { n } \hat { u } _ { i } X _ { i } = 0$

(Requires Appendix material) A necessary and sufficient condition to derive the OLS estimator is that the following two conditions hold: $\sum _ { i = 1 } ^ { n } \hat { u } _ { i } = 0 \text { and } \sum _ { i = 1 } ^ { n } \hat { u } _ { i } X _ { i } = 0$
Show that these conditions imply that $\sum _ { i = 1 } ^ { n } \hat { u } _ { i } \hat { Y } _ { i } = 0$

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