(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

a) Prove that if u1, ... um are vectors in R^{n}, S = {u1,u2,...uk} and T = {u1,...uk, uk+1,...um} then span(S) [tex]\subseteq[/tex]span(T).

b) deduce also that if R^{n}= span(S), then R^{n}=span(T)

2. Relevant equations

3. The attempt at a solution

I think I got part a:

the span S is represented by linear combination c1u1 + c2u2 + ... ckuk

and the span T is represented by the linear combination

c1u1 + c2u2 + ... ckuk +... cmum

and since span(S) is contained in span(T)

span(S)[tex]\subseteq[/tex]span(T)

Does this look alright?

b) part b is giving me trouble

since span(S) = R^{n}, the entire set of linear combinations of the vectors {u1,u2,...uk} in set S forms a plane.

since span(S) is a subset of (T) which spans R^{n},

span(T) = R^{n}.

I don't feel like this right at all, and I really can't visualize in my head what's going on here. Could somebody please help me? Thanks.

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# Homework Help: Linear algebra proof and vectors

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