In solving the following problems, give clearly written and logically com-plete arguments; and make sure that the differences between the two problems are clear.
i) Let v1,v2,···vn be a list of non-zero vectors such that no vector in the list is a linear combination of its predecessors. Prove that these vectors form a linearly independent set.
ii) Suppose that W is a subspace of an n-dimensional vector space V and dim(W) = n. Prove that W = V.