Find a linearly independent set of vectors

Question

Find a linearly independent set of vectors that spans that same subspace of R³ as that spanned by the vectors 

[3,2,3],[9,8,3],[3,3,0]. 

 

The linearly independent set is?

Answer 1

2(3,3,0)+(3,2,3)=(9,8,3)

(3,3,0) and (3,2,3) are not linearly dependent.  The only linear combination of the two producing a third coordinate of zero is adding zero times each vector.