T/F a set containing single vector is lin. indep.

lin indep means that only 0 can be multiplied by the vector to get the **0**. I said that this statement is true iff V_{1} can't equal 0.

b) Every linear dependent set conatins the zero vector?

this means that c1, c2, and c3 can be multiplied by the v1,v2,v3.... and get the **0** with c1,c2,c3.... not having to be zero right? That means that this statement is True.

Thanks for your help

Re: T/F a set containing single vector is lin. indep.

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Originally Posted by

**burton1995** lin indep means that only 0 can be multiplied by the vector to get the **0**. I said that this statement is true iff V_{1} can't equal 0.

That statement doesn't even make sense. It talks about "the vector" but "independent" and "dependent" apply to **sets** of vectors, not individual vectors (a set containing **one** vector is "linearly independent" if and only that vector is not the 0 vector.)

Okay, I didn't notice the title specified "a set containing single vector" so my parenthetical statement applies.

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b) Every linear dependent set conatins the zero vector?

this means that c1, c2, and c3 can be multiplied by the v1,v2,v3.... and get the **0** with c1,c2,c3.... not having to be zero right? That means that this statement is True.

No, it doesnt. Look at the set {<1, 1, 1>, <2,2,2>}. -2<1, 1, 1>+ 1<2, 2, 2>= <0, 0, 0>.

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Thanks for your help

Re: T/F a set containing single vector is lin. indep.

your answer to (a) is correct...but why? put another way, is the set {0} linearly dependent?

your answer to (b) is incorrect: consider the set {(1,0),(1,0)}. this is a linearly dependent set but i don't see the 0-vector in it, do you?