TITLE: Prove or Disprove: Subspaces, and Bases
QUESTION [1 upvotes]: Prove or disprove:
If U is a subspace of a finite dimensional vector space V and B = {v1, . . . ,vn} is a basis
for V, then some subset of B is a basis for U.
So far, I don't know where to start. I could assume that since B is a basis, it is linearly independent, and thus, some subset of B, containing less vectors than B, could potentially be a basis for U, since U is a subspace of V, but I don't know how to go about proving this. 
Thanks

REPLY [1 votes]: It's not true.  Suppose $V=\mathbb R^2$  Let the basis be $(0,1),(1,0)$ and the subspace be generated by $(1,1)$

REPLY [0 votes]: Hint: if this statement is generally true, then it is true in the case $U$ is a one-dimensional subspace, i.e. it is just the span of a single vector.
If a subset of $B$ is then a basis for $U$, what does this tell you about the vectors in $B$?
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