I am reading my linear algebra book, and in the chapter on Spanning, I got the impression that for a set to span R^n, it must contain at least n vectors. I confirmed that by searching through the forums.(adsbygoogle = window.adsbygoogle || []).push({});

However, I've reached the chapter on Linear Independence and in one of the examples it shows that a set containing 2 vectors can span R^3. So now I'm totally confused. Any help will be appreciated.

Example in the book:

S1= {[1,0,1], [0,1,1]}, S2 = {[1,0,1], [0,1,1], [3,2,5]}. Book says S1 and S2 span R^3, and prefers S1 since its "more efficient".

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# Number of vectors needed to Span R^n

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