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Linear Algebra

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Set Independent or Not

LINALG-GELP1E

Suppose that:

$$S=\left \{ \left [\matrix { 1 \cr 2 \cr 3}\right ], \left [ \matrix { 0 \cr 0 \cr 0}\right ], \left [\matrix { -1 \cr 0 \cr 5}\right ]\right \}$$

Which of the following statements are true about $S$?

Select ALL that apply.

A

$S$ is a linearly dependent set.

B

$S$ is a linearly independent set.

C

$S$ is a linearly independent set but if we add the vector: $\left [\matrix { 3 \cr 2 \cr 1}\right ]$ to $S$, the set created will be linearly dependent.

D

$S$ is a linearly dependent set, but if we remove the vector: $\left [\matrix { 1 \cr 2 \cr 3}\right ]$ from $S$, the set created will be linearly independent.