Answer to Question #94026 in Quantitative Methods for Joshua

Question

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

Answer 1

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.