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Back to Linear independence

Exercise 5.2.5

Avg difficulty 3.0

Are the following vectors linearly independent? If not, write one of them as a linear combination of the others.

u=[131],v=[142],w=[11−1].\mathbf{u}=\left[\begin{array}{r}1\\ 3\\ 1\end{array}\right],\quad\mathbf{v}=\left[\begin{array}{r}1\\ 4\\ 2\end{array}\right],\quad\mathbf{w}=\left[\begin{array}{r}1\\ 1\\ -1\end{array}\right].

Selinger, Matrix Theory and Linear Algebra, Spans, linear independence, and bases in Rn, Linear independence, Exercise 5.2.5

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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.