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Exercise 9.2.9

Avg difficulty 3.0

Assume $\mathbf{u},\mathbf{v},\mathbf{w}$ are linearly independent elements of some vector space $V$ . Consider the set of vectors

\textstyle R=\left\{2\mathbf{u}-\mathbf{w},~{}\mathbf{w}+\mathbf{v},~{}3\mathbf{v}+\frac{1}{2}\mathbf{u}\right\}.

Determine whether $R$ is linearly independent.

Selinger, Matrix Theory and Linear Algebra, Vector spaces, Linear combinations, span, and linear independence, Exercise 9.2.9

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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.