Suppose that you want to find the unique polynomial, y = f(x), of degree ≤ 6 that interpolates the 7 points (-2, 1), (-1, 3), (1, -4), (2, -6), (3, -1), (4, 3), (6, -2). (a) Write down the linear system that you need to solve to find the coefficients of this polynomial, and the augmented matrix of this system. (b) Solve the system from part (a) to find the coefficients of the polynomial (rounded to 3 decimal places) and write down the polynomial.
Suppose that you want to find the unique polynomial, y = f(x), of degree ≤ 6 that interpolates the 7 points (-2, 1), (-1, 3), (1, -4), (2, -6), (3, -1), (4, 3), (6, -2). (a) Write down the linear system that you need to solve to find the coefficients of this polynomial, and the augmented matrix of this system. (b) Solve the system from part (a) to find the coefficients of the polynomial (rounded to 3 decimal places) and write down the polynomial.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 15EQ
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