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Let V be a vector space having dimension n, and let S be a subset of V that generates V
Chapter 1, Problem 20(choose chapter or problem)
QUESTION:
Let V be a vector space having dimension n, and let S be a subset of V that generates V. (a) Prove that there is a subset of S that is a basis for V. (Be careful not to assume that S is finite.) (b) Prove that S contains at least n vectors.
Questions & Answers
QUESTION:
Let V be a vector space having dimension n, and let S be a subset of V that generates V. (a) Prove that there is a subset of S that is a basis for V. (Be careful not to assume that S is finite.) (b) Prove that S contains at least n vectors.
ANSWER:Step 1 of 2
Given:
Statement:a vector space is infinite-dimensional if and only if it contains an infinite linearly independent subset.