b$)$ Derive Newton$-$Cote quadrature formula and use it to derive Simpson's three$-$eight rule for numerical integration.

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c$)$ Would you advice the engineer to solve the above linear system using any of the iterative solution technique? Explain.

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d$)$ Given the relation $R=\{(1,2),(2,3)\}$ on the set $A=\{1,2,3\}.$ What is the minimum number of ordered pairs which when added to $R$ make it an equivalence relation? Discuss your reasoning.

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