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Proof of the replacement theorem, one of the most important theorems in linear algebra. It intuitively says that any linearly independent set can be extended to be a spanning set. It is used, for example, to show that the notion of dimension is well-defined. The proof is absolutely beautiful and requires use of the intruder theorem. Enjoy!
Replacement Theorem Video: • Replacement Theorem
Intruder Theorem Video: • Intruder Theorem
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