The task is to construct the natural cubic spline for the data provided in the tables below. You may use a matrix calculator to row reduce any matrices.**Table A:**| x | f(x) ||-----|-----------|| 0.8 | 0.22363362|| 1.0 | 0.65809197|**Table B:**| x | f(x) ||-----|-----------|| 0.1 | -0.29004996|| 0.2 | -0.56079734|| 0.3 | -0.81401972|The objective is to apply cubic spline interpolation to the given sets of discrete data points in tables A and B.

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Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Consider the following points.(−1, 5), (0, 0), (1, 1), (4, 52)(a)Write the augmented matrix that can be used to determine the polynomial function of least degree whose graph passes through the given points. 11 Correct: Your answer is correct. −1 21 Correct: Your answer is correct. 3-1 Correct: Your answer is correct. 45 Correct: Your answer is correct. 51 Correct: Your answer is correct. 0 60 Correct: Your answer is correct. 70 Correct: Your answer is correct. 80 Correct: Your answer is correct.91 Correct: Your answer is correct. 1 101 Correct: Your answer is correct. 111 Correct: Your answer is correct. 121 Correct: Your answer is correct.131 Correct: Your answer is correct. 4 1416 Correct: Your answer is correct. 1564 Correct: Your answer is correct. 1652 Correct: Your answer is correct.Determine the polynomial function of least degree whose graph passes through the given points.p(x) =
Use a graphing calculator to find the inverse of the matrix, if it exists.
Set up an augmentation matrix that would help to find the interpolating polynomial of degree at most 3 that passes through the points (0, 4), (1, 10), (–2,3), and (3, – 14). You DO NOT need to find the actual polynomial.
Please show every step. Please DO NOT skip a step. It is hard to follow or assume the step you took to solve the problem when steps are skipped.

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Construct the natural cubic spline for the data in each of the following tables. You may use a matrix calculator to row reduce any matrices. A. x f(x) 0.8 0.22363362 1.0 0.65809197