How to find the Basis?

Question

Find the Subspace of W of R^4 spanned by the following vectors and dimensions of W.

[-2]. [4]. [1]. [2]

[-1]. [2]. [2]. [1]

[-2]. [4]. [2]. [2]

[2], [-4], [2], [1],

Basis?

I answered the dimension which is (3)

Answer 1

If you put your matrix in RREF you should have 3 pivot points and the last row be all zeros. This means one of the vectors is a linear combination of the other 3. Meaning 3 of the vectors are linearly independent hence form a basis for the span of the 4 vectors.