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For each of the following statements, decide whether it is true or false. Note that you are being asked whether the given statements are true or false in all possible cases, not just for particular vectors or sets of vectors.
1. If {u1,...,u3} and {w1,...,w3} are two linearly independent sets in R3, then span{u1,...,u3} = span{w1,...,w3}.
2. Every set of 3 vectors in R4 is linearly independent.
3. Every subset of Rn which contains a linearly independent set is linearly independent.
4. If W is a subspace of Rn and u1,u2,...,uk are linearly independent vectors in W, then dim(W) >=k.
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