Let V be a vector space over a field F, and let S ={ i |i
Question:
Let V be a vector space over a field F, and let S ={αi |i ∈ I} be a nonempty collection of vectors in V.
a. Using Exercise 16(b), define the subspace of V generated by S.
b. Prove that the vectors in the subspace of V generated by S are precisely the (finite) linear combinations of vectors in S. (Compare with Theorem 7.6.)
Data from Exercise 16(b)
Prove that an intersection of subspaces of V is again a subspace of V over F.
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