Let X be the design matrix used to find the least-squares line to fit data (x 1
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Let X be the design matrix used to find the least-squares line to fit data (x1y1),.....(xn,yn). Use a theorem in Section 6.5 to show that the normal equations have a unique solution if and only if the data include at least two data points with different x-coordinates.
Data From Section 6.5
Transcribed Image Text:
Let A be an m x n matrix. The following statements are logically equivalent: a. The equation Ax = b has a unique least-squares solution for each b in R™. b. The columns of A are linearly independent. c. The matrix ATA is invertible. When these statements are true, the least-squares solution x is given by x = (A¹A)-¹A¹b
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Related Book For
Linear Algebra And Its Applications
ISBN: 9781292351216
6th Global Edition
Authors: David Lay, Steven Lay, Judi McDonald
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