Theorem: A subset B = {v1, v2, ..., vk} of a vector space V is a base for V if and only if for every vector v in V there exist unique scalars c1, c...
Theorem: A subset B = {v1, v2, ..., vk} of a vector space V is a base for V if and only if for every vector v in V there exist unique scalars c1, c2, ..., ck such that v = c1 v1 + c2 v2 + ... + ck vk.
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