Given a set of non zero vectors u v w t State all possible d

Given a set of non zero vectors {u, v, w, t}. State all possible dimensions at the vector space V = span{u, v, w, t}.

Solution

The possible dimesions of the vector space are 1(since we have non zero vectors), or 2(when three linearly dependent and 1 linearly independent vector is present), or 3 (when two linearly dependent and 2 linearly independent) or 4 (when all all linealry independent.)

so the answer is 1,2,3,4