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Exercise 5.1.3

Avg difficulty 3.0

Describe the span of the following vectors in R4\mathbb{R}^{4}:

u1=[11−1−1],u2=[5110],u3=[0−221],u4=[3111].\mathbf{u}_{1}=\left[\begin{array}{r}1\\ 1\\ -1\\ -1\end{array}\right],\quad\mathbf{u}_{2}=\left[\begin{array}{r}5\\ 1\\ 1\\ 0\end{array}\right],\quad\mathbf{u}_{3}=\left[\begin{array}{r}0\\ -2\\ 2\\ 1\end{array}\right],\quad\mathbf{u}_{4}=\left[\begin{array}{r}3\\ 1\\ 1\\ 1\end{array}\right].

Selinger, Matrix Theory and Linear Algebra, Spans, linear independence, and bases in Rn, Spans, Exercise 5.1.3

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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.