Lagrange Polynomals are defined by:(adsbygoogle = window.adsbygoogle || []).push({});

l_{j}(t)= (t-a_{0}) ....(t-a_{j-1})(t-a_{j+1})...(t-a_{n}) / (a_{j}-a_{0})...(a_{j}-a_{j-1})(a_{j}-a_{j+1})...(a_{j}-a_{n})

A) compute the lagrange polynomials associated with a_{0}=1, a_{1}=2, a_{2}=3. Evaluate l_{j}(a_{i}).

B) prove that (l_{0}, l_{1}, .... l_{n}) form a basis for R[t] less than or equal to n.

C) Deduce the Lagrange interpolation formula.

Thanks!!

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# Lagrange Polynomials Questions

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