Linearly independent

[mathsforumhelp]

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.

[jemidiah]

People usually don't directly answer homework problems in these forums. Also, with the other topics you posted, if you don't know how to do any of them you'd get much more out of a face-to-face talk with someone who knows linear algebra well than out of scattered forum responses.

Good luck.