state all possible dimensions os the vector space 8 Given a

state all possible dimensions os the vector space

8. Given a set of nonzero vectors tu, v, w t. State all possible dimensions of the vector space V-Span(u, v, w, t. Explain your answer,

Solution

Since these are non zero vectors so smallest dimension can be equal to 1 in case all vectors are multiples of each other

And largest can be 4 where u,v,w,t are linearly independent vectors

V can also have dimension 2 or 3 depending on whether we have only 2 or 3 linearly independent vectors in the set.