# Is this Vector-set Linear dependent?

1. Apr 25, 2012

### NorwegianStud

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.

2. Apr 25, 2012

### hamsterman

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.