Step 1:
To determine if the vectors are linearly independent, we need to see if there exist constants \( c_1, c_2, c_3 \) not all zero such that:
\[ c_1 \begin{bmatrix} 7 \\ 0 \\ 0 \end{bmatrix} + c_2 \begin{bmatrix} 9 \\ 4 \\ -16 \end{bmatrix} + c_3
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