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Exercise 11.5.2

Avg difficulty 3.0

Find the least squares approximation for the system of equations

[−121−10−1202002122][xyz]=[113−24].\left[\begin{array}{rrr}-1&2&1\\ -1&0&-1\\ 2&0&2\\ 0&0&2\\ 1&2&2\\ \end{array}\right]\left[\begin{array}{c}x\\ y\\ z\end{array}\right]=\left[\begin{array}{r}1\\ 1\\ 3\\ -2\\ 4\end{array}\right].

Selinger, Matrix Theory and Linear Algebra, Inner product spaces, Application: Least squares approximations and curve fitting, Exercise 11.5.2

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Adapted from Matrix Theory and Linear Algebra © 2017–2026 Peter Selinger, Lyryx Learning, and Ken Kuttler. Licensed under CC BY 4.0. Source: Matrix Theory and Linear Algebra. Imported at revision d74bc3a.