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

Consider a set of vectors:

S = {v[itex]_{1}[/itex],v[itex]_{2}[/itex],v[itex]_{3}[/itex],v[itex]_{4}[/itex][itex]\subset[/itex] ℝ[itex]^{3}[/itex]

a) Can S be a spanning set for ℝ[itex]^{3}[/itex]? Give reasons for your answer.

b) Will all such sets S be spanning sets? Give a reason for your answer.

3. The attempt at a solution

a) Yes, because a linear combination of these vectors can form any given vector in ℝ[itex]^{3}[/itex].

b) Yes, don't really know a reason besides something similar to the one above, I can't see why not.

I'm not really sure of these answers, can anyone confirm this, or given any insight to understand this better?

Cheers

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# Vectors - Spanning sets

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