Answer to Question #94026 in Quantitative Methods for Joshua

Question #94026
9.One of these describes the Lagrange’s interpolating polynomial P(x)
a.\\(p(x) = L_{1}(x)f_{0} + L_{2}(x)f_{1} + L_{3}(x)f_{2} + L_{4}(x)f_{3}\\)
b.\\(P(x) = L_{0}(x)f_{0} + L_{1}(x)f_{1} + L_{2}(x)f_{2} + L_{3}(x)f_{3}\\)
c.\\(P(x) = L_{0}(x)f_{3} + L_{1}(x)f_{2} + L_{2}(x)f_{1} + L_{3}(x)f_{0}\\)
d.\\(P(x) = L_{0}(x)f_{3} + L_{1}(x)f_{2} + L_{2}(x)f_{1} + L_{3}(x)f_{0}\\)

10.One of these is a method of solving system of linear equations:
a.Square Method
b.Inverse method
c.Lagrange Method
d.Transformation Method
1
Expert's answer
2019-09-11T11:11:51-0400

9.b) P(x) = L0(x)f0 + L1(x)f1 + L2(x)f2 + L3(x)f3

The Lagrange interpolating polynomial is the polynomial that is given by:


where


10.b) Inverse Method

Inverse method is a method of solving system of linear equations.

To solve a sytem, we should define a matrix of coefficients, then calculate the inverse of the matrix and perform a matrix multiplication.


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