Thread: Algebra Proofs

Hi everyone,

I am stuck on two problems, involving vector/matrix proofs: I think I would have to put these into a matrix of some sort, but I am unsure how to interpret it further. Some insight would be helpful

Let Q= set{v1, v2, ..., vq} in r^n

1. Prove that if n<q, then there exists a vector in R^n that is not in the element of Span Q..

2. Prove that if n>q, then Q is linearly independent.

THanks!

What you've written makes no sense. You say "if k< q" but there is NO "k" in the "let Q= ..." part. Did you mean
"Let Q= set{v1, v2, ..., vq} in R^k?"

If so, then you will need to use the fact that R^k has dimension k.

Sorry, I meant if q<n and q>n.