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Linear Algebra

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Linear Dependence - Set of Non-Zero Vectors

LINALG-G83K55

A set of non-zero vectors $\vec v_1, \ldots, \vec v_n$ is linearly dependent if:

A

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

B

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

C

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

D

There exist $c_1\neq 0, c_2\neq 0, \ldots, c_n\neq 0$ such that: $c_1\vec v_1+\ldots + c_n \vec v_n=\vec 0$

E

There exist $c_1, c_2, \ldots ,c_n$ not all equal to zero, such that: $c_1\vec v_1+\ldots +c_n \vec v_n=\vec 0$

F

Both Choice 'D' and 'E' are correct.

G

Both Choice 'B' and 'E' are correct.