Determine whether the vectors $ \vec{v_1} = \left(0,~0\right) $ and $ \vec{v_2} = \left(0,~0\right) $ are linearly independent or dependent.
Answer
The vectors are linearly dependent.
Explanation
To check if two vectors are dependent we solve the determinant:
$$ D = \left| \begin{array}{cc} 0 & 0 \\ 0 & 0 \end{array} \right| = 0\cdot0 -0\cdot0 = 0 - 0 = 0 $$Since $ D = 0$ we conclude that $ v_1 $ and $v_2$ are linearly dependent.
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