Prove Linear Dependence for Set of Vectors w/ Zero Vector

eyehategod · Nov 4, 2007

I have to prove that any set of vectors containing the zero vector is linearly dependent.
How can I approach this?

sdobbers · Nov 4, 2007

(C1)(X1) + (C2)(X2) + ... + (Cn)(Xn) = 0

Take X1 = 0 vector; and all other constants besides C1 to be zero.

(C1)(0) + (0)(X2) + ... +(0)(Xn) = 0

In this case, C1 does not have to be equal to 0, it could be any number. In order for them to be independent, c1=c2=cn=0; since c1 does not equal 0 therefore they're dependent.

This is the way my professor described it to me, hopefully this helps.

eyehategod · Nov 4, 2007

thats it? thanks a lot bro, I get it now. \m/

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