A First Course in Linear Algebra · Problem LI.C23

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. {[1−2253],[3312−4],[212−11],[10122]}\left\{ \begin{bmatrix} 1 \\ -2 \\ 2 \\ 5 \\ 3 \end{bmatrix}, \begin{bmatrix} 3 \\ 3 \\ 1 \\ 2 \\ -4 \end{bmatrix}, \begin{bmatrix} 2 \\ 1 \\ 2 \\ -1 \\ 1 \end{bmatrix}, \begin{bmatrix} 1 \\ 0 \\ 1 \\ 2 \\ 2 \end{bmatrix} \right\}

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