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Exercise 11.3.3

Avg difficulty 3.0

In $\mathbb{R}^{4}$ with the usual dot product, find an orthogonal basis for

\operatorname{span}\left\{\left[\begin{array}{c}1\\ 0\\ 1\\ 0\end{array}\right],~{}\left[\begin{array}{c}1\\ 3\\ 1\\ -1\end{array}\right],~{}\left[\begin{array}{c}2\\ 4\\ 2\\ 2\end{array}\right]\right\}.

Selinger, Matrix Theory and Linear Algebra, Inner product spaces, The Gram-Schmidt orthogonalization procedure, Exercise 11.3.3

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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.