The set of vectors $\left\{ \begin{pmatrix} 3 \\ 7 \end{pmatrix}, \begin{pmatrix} k \\ -2 \end{pmatrix} \right\}$ is linearly independent.  Find all possible values of $k.$  Enter your answer as an interval.
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The set of vectors $\left\{ \begin{pmatrix} 3 \\ 7 \end{pmatrix}, \begin{pmatrix} k \\ -2 \end{pmatrix} \right\}$ is linearly independent.  Find all possible values of $k.$  Enter your answer as an interval.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
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user
\left( -\infty, -\frac{6}{7} \right) \cup \left( -\frac{6}{7}, \infty \right)
The set of vectors $\left\{ \begin{pmatrix} 3 \\ 7 \end{pmatrix}, \begin{pmatrix} k \\ -2 \end{pmatrix} \right\}$ is linearly independent.  Find all possible values of $k.$  Enter your answer as an interval.
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