A First Course in Linear Algebra · Problem LI.C24

Vectors — Robert Beezer

Mathematics — Linear Algebra · linear-independence

Problem

Determine if the set of vectors below is linearly independent or linearly dependent. When the set is linearly dependent, exhibit a nontrivial relation of linear dependence. {[12−101],[32−122],[44−223],[−12−1−20]}\left\{ \begin{bmatrix} 1 \\ 2 \\ -1 \\ 0 \\ 1 \end{bmatrix}, \begin{bmatrix} 3 \\ 2 \\ -1 \\ 2 \\ 2 \end{bmatrix}, \begin{bmatrix} 4 \\ 4 \\ -2 \\ 2 \\ 3 \end{bmatrix}, \begin{bmatrix} -1 \\ 2 \\ -1 \\ -2 \\ 0 \end{bmatrix} \right\}

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