SOLUTION: What is a basis?

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A basis B of a vector space V satisfies:
(1) The set of all vectors in B are linearly independent
This means: for any vectors v1,v2,..,vn in B and scalars ai
a1v1+ a2v2+..+anvn = 0 implies ai= 0 for all i.
(2) Any vector v n V can be expressed as a linear combination of
vectors of B.
That is, the set B can generate (span) the whole space V.

Keny