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Carl140
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Homework Statement
Let V be a vector space over a field K. Let S be a set of vectors of V,
S= {e_i : i in J} (i.e e_i in V for each i in J) where J is an index set.
Prove that if S satisfies the following property, then S must be a basis.
The property is:
For every vector space W over the field K and for every function f: S-> W there exists
a unique linear transformation T: V-> W such that T restricted to S = f.
The Attempt at a Solution
I really have no clue how to start this, of course I must prove its linearly independent
and its spans V.