A First Course in Linear Algebra · Problem LI.C25

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. {[213−12],[4−2132],[10−70104]}\left\{ \begin{bmatrix} 2 \\ 1 \\ 3 \\ -1 \\ 2 \end{bmatrix}, \begin{bmatrix} 4 \\ -2 \\ 1 \\ 3 \\ 2 \end{bmatrix}, \begin{bmatrix} 10 \\ -7 \\ 0 \\ 10 \\ 4 \end{bmatrix} \right\}

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