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.
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!