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I have this set of vectors:

(1,1) , (-2,-2) , (0,0) , (3,-2)

I need to say if it linearly dependent, and I need to find the maximum size of the subset of this set, which is linearly independent.

What I think, is that as long as (0,0) is there, it must be dependent. In addition, (1,1) and (-2,-2) are also dependent. Thus if I had to guess, I would say the maximum size is 2 vectors, (3,-2) and either (1,1) or (-2,-2). My question is, am I right, or am I missing something ?

Thanks !