1. The problem statement, all variables and given/known data Suppose that E,F are sets of vectors in V with [itex]E \subseteq F[/itex]. Prove that if E is linearly dependent, then so is F. 3. The attempt at a solutionRead post #2. This proof, I think, was incorrect. If we suppose that E is linearly dependent, then we know that there exists [itex]E_1,...,E_n[/itex] distinct vectors such that, [itex]e_1 E_1 + ... + e_n E = \vec0[/itex], where e1,...,en are numbers. Thus, we know [itex]\vec0 \in E[/itex]. Since [itex]E \subseteq F[/itex], [itex]\vec0 \in F[/itex]. Any set containing the zero-vector must certainly be linearly dependent since [itex]n \vec0 = \vec0[/itex], where n is any number. Thus, if E is linearly dependent, then F is linearly dependent. Sound about right?