- #1

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## Main Question or Discussion Point

So I was reading my textbook and I confused myself about a theorem

Where if S={v,v

It doesnt make sense to me because if we look at 2 vectors in ℝ

we have u=(u1,u2,u3) and v=(v1,v2,v3)

So i do k1(u1,u2,u3)+k2(v1,v2,v3)=0

If i use a matrix:

u1 v1 0

u2 v2 0

u3 v3 0

Then it would seem to me as both vectors would be linearly dependent, no?

Where if S={v,v

_{2},.....,v_{r}} and in ℝ^{n}then if r>n, then it is linearly dependentIt doesnt make sense to me because if we look at 2 vectors in ℝ

^{3}(lets say u and v)we have u=(u1,u2,u3) and v=(v1,v2,v3)

So i do k1(u1,u2,u3)+k2(v1,v2,v3)=0

If i use a matrix:

u1 v1 0

u2 v2 0

u3 v3 0

Then it would seem to me as both vectors would be linearly dependent, no?