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Suppose we are asked to fit a straight line to the following data m 1 -2 1 1 -1 1 so that mx + c = y Write the system of linear equations mx + c y. Determine the matrix A. and vector b to write this problem as a matrix equation A x b (a)

Suppose we are asked to fit a straight line to the following data m 1 -2 1 1 -1 1 so that mx + c = y Write the system of linear equations mx + c y. Determine the matrix A. and vector b to write this problem as a matrix equation A x b (a)

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Suppose we are asked to fit a straight line to the following data m 2 1 3 -2 1 2 -1 1 so that mx + c = y Write the system of linear equations mx + c = y. Determine the matrix A. and vector b to write this problem as a matrix equation A x b Describe the relationship between the vector b and the column space of (a) (b) A. Given that the matrix equation in part (a) has no solution, a least squares solution is sought by looking for a vector x that minimises the error e = Ax - b. This means that e is perpendicular to the columns of A. Show that this fact leads to the normal equations: (c) ATA X = ATb Use the matrix equation in part (c) to determine the associated normal equations and the least squares solution, x, for the matrix equation in part (a). (d)
Transcribed Image Text:Suppose we are asked to fit a straight line to the following data m 2 1 3 -2 1 2 -1 1 so that mx + c = y Write the system of linear equations mx + c = y. Determine the matrix A. and vector b to write this problem as a matrix equation A x b Describe the relationship between the vector b and the column space of (a) (b) A. Given that the matrix equation in part (a) has no solution, a least squares solution is sought by looking for a vector x that minimises the error e = Ax - b. This means that e is perpendicular to the columns of A. Show that this fact leads to the normal equations: (c) ATA X = ATb Use the matrix equation in part (c) to determine the associated normal equations and the least squares solution, x, for the matrix equation in part (a). (d)
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