Question

Let S be a linearly independent set in a vector space V . If x belongs to V
and x does not belong to span(S), then prove that span(S) U {x} is linearly independent.

Answer 1

Answer:

Theorem: If S is any subset of V , the span of S is the smallest linear subspace of V containing S. Example Let ... are not “linearly independent.” Definition ... If x = 0, this equation can be solved for v, showing.