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Exercise 11.5.1

Avg difficulty 3.0

Find the least squares approximation for the system of equations

x + 2y + 2z = 5,x + y − z = 11,x + 2y − z = −18,2x − y + 2z = 0.\begin{array}{rcrcrcr}x~{}&+~{}&2y~{}&+~{}&2z~{}&=~{}&5,\\ x~{}&+~{}&y~{}&-~{}&z~{}&=~{}&11,\\ x~{}&+~{}&2y~{}&-~{}&z~{}&=~{}&-18,\\ 2x~{}&-~{}&y~{}&+~{}&2z~{}&=~{}&0.\\ \end{array}

Selinger, Matrix Theory and Linear Algebra, Inner product spaces, Application: Least squares approximations and curve fitting, Exercise 11.5.1

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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.