Thread: 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 V₁ 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

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 V₁ 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.

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>.

Thanks for your help

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?