# Thread: Vector Space, Basis

1. ## Vector Space, Basis

Let V be an n-dimensional vector space. Let S =
{v1......vn} be a linearly-independent subset of V consisting of n vectors.
Show that it is a basis.

2. ## Re: Vector Space, Basis

Originally Posted by andy12392
Let V be an n-dimensional vector space. Let S =1......vn} be a linearly-independent subset of V consisting of n vectors. Show that it is a basis.
Please either post some of your own work on the problem or explain what you do not understand about the question.
What does it mean to say that a set of vectors is linearly-independent?

3. ## Re: Vector Space, Basis

Originally Posted by Plato
Please either post some of your own work on the problem or explain what you do not understand about the question.
What does it mean to say that a set of vectors is linearly-independent?
Im not entirely sure what linearly independent means. But i think for it to be a basis it has to be both linearly independent and be a spanning set. Since we are told that S is linearly independent all thats left to do is prove that L(S) = V but im really not sure where to begin

4. ## Re: Vector Space, Basis

Originally Posted by andy12392
Im not entirely sure what linearly independent means. But i think for it to be a basis it has to be both linearly independent and be a spanning set. Since we are told that S is linearly independent all thats left to do is prove that L(S) = V but im really not sure where to begin
Pray tell us how you expect to work a question out not knowing the basic definitions. Do you know any fact about linearly independent sets and the dimension of the v-space?