- #1
pollytree
- 14
- 0
Homework Statement
V is a subspace of Rn and S={v1,...,vk} is a set of linearly independent vector in V. I have to prove that any list of linearly independent vectors can be extended to a basis for V.
Homework Equations
None that I can think of.
The Attempt at a Solution
So to be a basis, the vectors must be linearly independent (which is given) and span V. I think we also have to show that the number of elements in the basis is equal to the dimension of V. We have a hint that says we can prove the statement above by adding vectors which are not in span S one at a time until we span all of V and arguing that the result is linearly independent.
But I'm not really sure where to begin on this question. Any help would be great! Thanks :D