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Back to Linear independence

Exercise 5.2.3

Avg difficulty 3.0

Use the method of Theorem 5.21 to determine whether the following vectors are linearly independent. If they are linearly dependent, find a non-trivial linear combination of the vectors that is equal to 0\mathbf{0}.

u1=[232],u2=[−102],u3=[−3−4−2],u4=[562].\mathbf{u}_{1}=\left[\begin{array}{r}2\\ 3\\ 2\end{array}\right],\quad\mathbf{u}_{2}=\left[\begin{array}{r}-1\\ 0\\ 2\end{array}\right],\quad\mathbf{u}_{3}=\left[\begin{array}{r}-3\\ -4\\ -2\end{array}\right],\quad\mathbf{u}_{4}=\left[\begin{array}{r}5\\ 6\\ 2\end{array}\right].

Selinger, Matrix Theory and Linear Algebra, Spans, linear independence, and bases in Rn, Linear independence, Exercise 5.2.3

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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.