Is this Vector-set Linear dependent?

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The discussion centers on the linear dependence of a vector set defined by the matrix: 1 -1 0; -1 1 2; 0 8 4; 4 2 0. The conclusion is that the set is indeed linearly dependent because it contains more vectors (four) than the dimensions of the space (three). This is supported by the principle that if a set of vectors exceeds the dimensionality of the space, at least one vector can be expressed as a linear combination of the others.

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1 -1 0
-1 1 2
0 8 4
4 2 0

v1= {1, -1, 0} and so on.

Is it linear dependent?

I think it is, since I read somewhere that if the Vector have less dimensions than it have vectors in the set then it's linear dependent. Or is it? I'm a bit confused.
 
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Yes. Are you aware that a set n of linearly independent vectors define a n dimensional vector space? That is, if you have 3 independent vectors, you can build any other 3d vector from them. If some 4 vectors are independent, than any 3 must be independent too. This follows from the definition of independence. If 3 vectors are linearly independent then the fourth must be a linear product of them.
 

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