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Prove the following generalization of Theorem 1.9 (p. 44): Let Si and S2 be subsets of a
Chapter 1, Problem 6(choose chapter or problem)
Prove the following generalization of Theorem 1.9 (p. 44): Let Si and S2 be subsets of a vector space V such that Si C S2. If Si is linearly independent and S2 generates V, then there exists a basis ft for V such that Si C ft C S2. Hint: Apply the maximal principle to the family of all linearly independent subsets of S2 that contain Si, and proceed as in the proof of Theorem 1.13.
Questions & Answers
QUESTION:
Prove the following generalization of Theorem 1.9 (p. 44): Let Si and S2 be subsets of a vector space V such that Si C S2. If Si is linearly independent and S2 generates V, then there exists a basis ft for V such that Si C ft C S2. Hint: Apply the maximal principle to the family of all linearly independent subsets of S2 that contain Si, and proceed as in the proof of Theorem 1.13.
ANSWER:Step 1 of 3
Consider 
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To prove:
The aim is to show that if 
