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Back to Linear independence

Exercise 5.2.6

Avg difficulty 3.0

Find a linearly independent set of vectors that has the same span as the given vectors.

u1=[203],u2=[135],u3=[338],u4=[3−31].\mathbf{u}_{1}=\left[\begin{array}{r}2\\ 0\\ 3\end{array}\right],\quad\mathbf{u}_{2}=\left[\begin{array}{r}1\\ 3\\ 5\end{array}\right],\quad\mathbf{u}_{3}=\left[\begin{array}{r}3\\ 3\\ 8\end{array}\right],\quad\mathbf{u}_{4}=\left[\begin{array}{r}3\\ -3\\ 1\end{array}\right].

Selinger, Matrix Theory and Linear Algebra, Spans, linear independence, and bases in Rn, Linear independence, Exercise 5.2.6

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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.