Math  /  Algebra

QuestionQuestion 3 [10 points] For each of the following sets of vectors, determine whether it is linearly independent or linearly dependent. If it is dependent, give a non-trivial linear combination of the vectors yielding the zero vector. Give your combination as an expression using u,vu, v, and ww for the vector variables u,v\mathbf{u}, \mathbf{v}, and w\mathbf{w}. a) u=[132]v=[373]w=[286]\mathbf{u}=\left[\begin{array}{l}1 \\ 3 \\ 2\end{array}\right] \mathbf{v}=\left[\begin{array}{c}-3 \\ -7 \\ -3\end{array}\right] \mathbf{w}=\left[\begin{array}{c}-2 \\ -8 \\ -6\end{array}\right] pts: 0/40 / 4 ppts: 0/40 / 4 ppts: 1 / 4 < Select an answer> b) u=[121]v=[172]w=[268]\mathbf{u}=\left[\begin{array}{c}1 \\ -2 \\ -1\end{array}\right] \quad \mathbf{v}=\left[\begin{array}{c}-1 \\ 7 \\ -2\end{array}\right] \quad \mathbf{w}=\left[\begin{array}{c}-2 \\ -6 \\ 8\end{array}\right] pts: 0/40 / 4 ppts: 0/40 / 4 pts: 1 / 4 < Select an answer >

Studdy Solution
Since we only found the trivial solution, the vectors are linearly independent. There is no non-trivial linear combination that yields the zero vector.
In conclusion: a) The vectors are linearly dependent, with the non-trivial linear combination 2u - v - w = 0. b) The vectors are linearly independent.

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