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a) Suppose $S = \{v_1, v_2, v_3, v_4, v_5\}$, where

$v_1 = \left( \begin{array}{c} 1 \\ -1 \\ -1 \\ 2 \end{array} \right)$, $v_2 = \left( \begin{array}{c} 1 \\ -1 \\ 0 \\ -1 \end{array} \right)$, $v_3 = \left( \begin{array}{c} 5 \\ -5 \\ -2 \\ 1 \end{array} \right)$, $v_4 = \left( \begin{array}{c} 1 \\ -1 \\ 1 \\ -4 \end{array} \right)$, $v_5 = \left( \begin{array}{c} 0 \\ 0 \\ 3 \\ -9 \end{array} \right)$,

Without doing any row operations, explain why $S$ is a linearly dependent set

I don't know how to start by just looking at it, all I can do is just Row Operation and see the leading columns then judge if it is linearly dependent or not.

Would someone please tell me how to judge if the set is a linearly dependent or independent set please?

Thank you.

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5 vectors, none of which are scalar multiples of any of the others, in a 4 dimensional space.

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  • $\begingroup$ I meant that they are not scalar multiples of each other $\endgroup$
    – user27182
    Feb 10, 2015 at 1:21

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