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What does it mean to say that vectors $\vec v_1, \vec v_2, \ldots, \vec v_n$ are linearly independent?

A

$c_1\vec v_1+\ldots+ c_n \vec v_n=\vec 0$ implies that all $c_i=0$.

B

$c_1\vec v_1+\ldots+ c_n\vec v_n=\vec 0$ implies that at least one $c_i=0$.

C

$c_1\vec v_1+\ldots+ c_n\vec v_n=\vec 0$ implies no $c_i=0$.

D

$c_1\vec v_1+\ldots+ c_n\vec v_n=\vec 0$ implies that all $\vec v_i=0$.

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