linear algebra span question

[peacefreak77]

I hope this is the right forum to post this in.

Anyway, I don't know how to do this problem.
Find a linearly independent set of vectors that spans the same subspace of
(these are vectors) [[3][-2][-1]],[[3][-5][1]],[[0][-3][2]].

I think that these are linearly dependent vectors because there are infinite solutions to Ac=0 (if you consider A the matrix formed by these three vectors). Meaning I can use parameters and write the solutions for vector c.

Because these are linearly dependent vectors, I know they don't span all of R^3. But I don't know how to solve for exactly what B's (from Ac=B) they do span. Consequently, I don't know how to write an independent set of vectors that spans the same subspace, and I don't understand how an independent set of vectors could span the same specific subspace of a linearly dependent set of vectors, since 3 linearly independent vectors span all R^3.

I know the answer consists of 2 vectors with three componants, but I don't have any idea how to find the set they're asking for.

 

[Unco]

Any two of those vectors are linearly independent so the span of the three vectors is equal to the span of any two of them. Confirm this with yourself by writing out a linear combination of three vectors and then using the fact that the third is a linear combination of the first two, arriving at a linear combination of two vectors.