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Back to Linear independence

Exercise 5.2.10

Avg difficulty 3.0

Here are some vectors.

u1=[11−2],u2=[22−4],u3=[27−4],u4=[57−10],u5=[1217−24].\mathbf{u}_{1}=\left[\begin{array}{r}1\\ 1\\ -2\end{array}\right],\quad\mathbf{u}_{2}=\left[\begin{array}{r}2\\ 2\\ -4\end{array}\right],\quad\mathbf{u}_{3}=\left[\begin{array}{r}2\\ 7\\ -4\end{array}\right],\quad\mathbf{u}_{4}=\left[\begin{array}{r}5\\ 7\\ -10\end{array}\right],\quad\mathbf{u}_{5}=\left[\begin{array}{r}12\\ 17\\ -24\end{array}\right].

Describe the span of these vectors as the span of as few vectors as possible.

Selinger, Matrix Theory and Linear Algebra, Spans, linear independence, and bases in Rn, Linear independence, Exercise 5.2.10

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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.