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How can you have a basis through the spanning set theorem? I thought the spanning set...

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Advance Math

How can you have a basis through the spanning set theorem? Ithought the spanning set has to be linear independent? Doesn't thespanning set theorem say that the vectors in the set are lineardependent as you can them as a linear combination of each other? AmI overthinking this or am I getting this wrong?

**UPDATED

I think I have the answer to my question, we use the theorem tobasically turn the set into a linearly independent set by gettingrid of the vectors we can write a combination of, correct?

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