Daniels Rowe
06/15/2024 · Middle School
Consider the vectors \( \vec{u}=\left[\begin{array}{c}-5 \\ 8 \\ -5\end{array}\right], \vec{v}=\left[\begin{array}{c}6 \\ 6 \\ -4\end{array}\right] \), and \( \vec{w}=\left[\begin{array}{c}-\frac{30}{7} \\ -\frac{108}{7} \\ k\end{array}\right] \). What value of \( k \) will make the set \( \{\vec{u}, \vec{v}, \vec{w}\} \) linearly dependent? You may submit your answer as a fraction, if necessary. \( k= \) \( \square \) makes the set linearly dependent.
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\( k = \frac{36}{7} \) makes the set linearly dependent.
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